Given an exponential graph that are concave up and the points (1,4) and (1, 16), give a possible formula of the function. I plugged the variables into the f(x)=b times a^x and got: 4= b times a^1 and 16=b times
41,653 results
math
Find the exponential function f(x)=Ca^x whose graph goes through the points (0,3) and (2,12).

college calc
Give a formula for the function illustrated using a vertical shift of an exponential function. The two points marked on the graph are A=(−1,17) and B=(1,2). The red horizontal line is given by y=1, and is a horizontal asymptote of the function. What is

Calculous
the figure shows the graph of F', the derivative of a function f. the domain of the function f is the set of all X such that 3< or equal to x

Calculus
Let g be a function that is defined for all x, x ≠ 2, such that g(3) = 4 and the derivative of g is g′(x)=(x^2–16)/(x−2), with x ≠ 2. a.Find all values of x where the graph of g has a critical value. b.For each critical value, state whether the

Mathematics, PreCalculus
Help needed! Find the base of the exponential function whose graph contains the given points. 1. (2,16) 2. (1,10) 3. (3,64) 4. (3,1/343) 5. (4,1/625) 6. (3/2,27)

Calculus
Consider the function f(x)=xe^2x. Find the intervals on which f(x) is concave up and the intervals where it is concave down. Show a sign graph. Please show work in detail so I can follow for future reference. Thanks!

calculus please help asap
true or false questions: a)The derivatives of the reciprocal trigonometric functions can be found using the chain rule and their related base functions. b) A sinusoidal function can be differentiated only if the independent variable is measured in radians.

math
find the base of the exponential function whose graph contains the given points. 1.( 4, 1/625) 2.(3/2, 27) 3.(3, 1/343)

math
If two quantities vary directly, which must be true of a graph showing the relationship between them? Select all that apply. A. The graph is a curve. B. The points on the graph are connected. C. The graph increases from left to right. D. The points of the

math
Give a formula for the exponential function . The two points marked on the graph are A=(−1−43) and B=(12). The red horizontal line is given by y=5, and is a horizontal asymptote of the function.

Please check my Calculus
1. Given f(x)=6/x, choose the correct statement A. The graph of f is concave upward on the interval (negative infinity, 0) B. The graph of f is concave downward on the interval (negative infinity, 0) C. The graph of f is concave upward on the interval

math
Find an exponential function of the form f(x) = C · a^x + D with horizontal asymptote y =1 whose graph contains the points (1,7)and (0,5).

calculus
Below is the graph of f '(x), the derivative of f(x), and has xintercepts at x = 3, x = 1 and x = 2 and a relative maximum at x = 1.5 and a relative minimum at x = 1.5. Which of the following statement is true? (it's a positive cubic function graphed

Calculus
Consider the function of defined by f(x)=x^3/34/x a. Find the X values for the points of inflection. b. Determine the intervals where the function of f is concave up and concave down.

Calculus
For the function below, determine the intervals of concavity: f(x)=xlnx I tried doing it but the second derivative would always be f''(x)=1/x, so it would be concave up at x>0 and concave down at x

calculus
The function y=f(x) graphed above is assumed to be a vertical shift of an exponential function. The two points marked on the graph are A= (1,31) and B= (1,1) . The red horizontal line is given by y= 1, and is a horizontal asymptote of the function. Give

Advanced Algebra
Find the exponential function of the form y=ax^b whose graph passes through the points (3, 1/27) and (0,1). I don't know where to begin with this problem??

Calculus
The graph of f ′(x) is continuous and decreasing with an xintercept at x = 0. Which of the following statements is false? (4 points) The graph of f has an inflection point at x = 0. The graph of f has a relative maximum at x = 0. The graph of f is

Algebra
Mary creates a table of values for a function and plots the points. She finds that the difference in the y values is the same. What kind of function did she graph? How can you tell if a graph is linear, quadratic, exponential or square root?

calculus
Let f (x) = x^2 + 5x14. Find the open intervals on which f is concave up (down). Then determine the xcoordinates of all inflection points of f 1. f is concave up on the intervals 2. f is concave down on the intervals 3. The inflection points occur at x

Calculus really quick check
The graph of f ′(x) is continuous and decreasing with an xintercept at x = 2. Which of the following statements must be true? Edit The graph of f has an inflection point at x = 2. The graph of f has a relative maximum at x = 2. The graph of f is always

physics
I'm making a graph of force vs stretch for springs. I have 7 data trials with the k (F = kx) ranging from 28 to 31, average is 29.6. Now I need to find the slope and write an equation for the graph. If I use the first two points to get the slope, I get a

help please!
f(x)=x+1/x Find all critical numbers. Find where the function is increasing and decreasing. Find critical points and identify each as a relative maximum, relative minimum, or neither. Find second order critical numbers and tell where the graph is concave

Algebra II
Use the equation of the exponential function whose graph passes through the points (0,2) and (2,50) to find the value of y when x = 2. I know the formula is y=ab^x but I don't know what numbers to plug in. Any help would be great. Thanks.

Calculus
For what values of x is the graph of the function f(x)= x^2e^x concave down. Give your answer using exact values

calculus
Consider the exponential function . Which of the following best describes the the graph of g? a. Concave up and increasing b. Concave up and decreasing c. Concave down and increasing d. Concave down and decreasing The rules are +constant, concave up, 

Calculus
Sketch the graph of the function that has the following properties. f is continuous on (infinity, infinity). points: (1,2), (0, 0), (1,0) f'(x)>0 at (infinity, 1) f'(1)=0 f'(x)0 on (1, infinity) f"(x)0 on (0, infinity) I'm having trouble graphing

Math (Calculus II) (Graph approximation)
Here is the link to the graph of f' in question: bit.ly/2oml70V I have a hard time trying to answer these kinds of questions when we're only given a graph of f'. a) Approximate the slope of f at x = 4. Explain. I believe the slope of f in this case would

Math
For y= (3x)/(2e^x+e^1), use graphing techniques to find the approximate intervals on which the function is: a) increasing b) decreasing c) concave up, d) concave down then find any e) local extrema f) inflection points

APCalculus
For the function y=2sin(x)cos^2(x) on [0, 2pi] find the following: Domain x and y intercepts Vertical asymptotes Horizontal asymptotes Symmetry F'(x) Critical numbers Increasing f(x) Decreasing f(x) Extrema F"(x) Possible points of inflection Concave up

grade 12 AP calculus
for f(x= 1/4x41/3x3+2x, use analytic method to find the exact intervals on which the function is a)increasing, b)decreasing, c)concave up, d)concave down, then find any e)local extreme values, f)inflection points

Math  Simple rational Function (check)
Consider the function f(x) = x/(x1) Are there any turning points? Explain how this could help you graph f(x) for large values of x? Ans: turning points is another word for checking the concavity, and therefore i find the second derivative and equate it to

Calc
For the function f(x) = 5x^6 + 6x^5  15x^4 a.) find where the function is increasing & decreasing b.) find where the graph if concave up & concave down c.) name all inflection points d.) find all relative extrema

Calculus
Given the function f(x)= x√(x+3), Indicate the domain of f(x): ………………………… What are the x – intercepts of the graph of f(x)? POINTS! ……………………………. Identify the critical points of f(x) (write pairs of coordinates,

Math
Find the intervals on which the function is increasing, decreasing, concave up, or concave down and find any local extreme values and inflection points. So I know how to do the above, but not with piece wise functions. Someone help me out? Y={3x^2, x=0} I

Math
If two quantities are directly, which must be true of a graph showing relationships between them? Select all that apply. A. The graph is a curve B. The point on the graph are connected C. The graph increases from left to right. D.the points of the graph

Calculus
Determine the open intervals on which the graph of f(x) = 7x^2 + 8x + 1 is concave downward or concave upward. The second derivative is just 14, so I don't know what to do with that.

MathCalculus
Let y = f(x) be the continuous function that satisfies the equation x^4  (5x^2)(y^2) + 4y^4 = 0 and whose graph contains the points (2,1) and (2,2). Let L be the line tangent to the graph of f at x = 2. (a) Find and expression for y'. (b) Write an

Calculus
Let f be the function defined for x >or= to 0 with f(0)=5 and f', the first derivative of f, give by f'(x)=e^(x/4)sin(x^2). A) Use the graph of f' to determine whether the graph of f is concave up, concave down, or neither on the interval 1.7

calculus
Please help me solve. I think increase = concave up and decrease = concave down? On the graph y = x^515x^3+10 for x what intervals is the function increasing, decreasing, concave up and concave down. Plot the critical points, plot and label the inflection

calculus
Let f (x) =7x5/x+3 . Find the open intervals on which f is concave up (down). Then determine the xcoordinates of all inflection points of f . 1. f is concave up on the intervals 2. f is concave down on the intervals 3. The inflection points occur at x =

Calc
The graph of f ′(x) is continuous and increasing with an xintercept at x = 0. Which of the following statements is false? The graph of f is always concave up. The graph of f has an inflection point at x = 0. The graph of f has a relative minimum at x =

Fullerton
Graph each function considering the domain, critical points, symmetry regions, where the function is increasing or decreasing, inflection points where the function is concave up or down, intercepts where possible and asymptote where applicable f(x)= x^4

calculus
Give a possible formula for the illustrated function using a vertical shift of an exponential function. The two points marked on the graph are A=(−172) and B=(10). The red horizontal line is given by y=−3, and is a horizontal asymptote of the function

Precalc
Are exponential equations the same as exponential functions? I am writing a summary of this year's PreCalculus lessons and one of the topics on the outline is "Exponential Equations", but on the lesson Power Points on my teacher's website there is only

Calculus
Suppose that f(x)=ln(3+x^2). Use interval notation to state when f(x) is concave up and concave down. Then find all inflection points for f(x).

algebra 2
Find an exponential function of the form y=ab^x whose graph passes through the points (2,1) and (3,2).

alg 2
write an exponential function whose graph passes throught the given points... (0,3)and (1,15)...(0,5)and(3,135)...(0,0.3)and(5,9.6)

algebra
For a fixed rate, a fixed principal amount, and a fixed compounding cycle, the return is an exponential function of time. Using the formula, , let r = 10%, P = 1, and n = 1 and give the coordinates (t, A) for the points where t = 0, 1, 2, 3, 4. Round your

Maths
Question – 1: The gradient of the graph of f(x) at any point is,ax^212x + 9, and the point,(2,3),is an inflection point of f(x). (a) Find the value of the real constant, a. Find the function f(x). (b) Find the stationary points of the function, then

a
For a fixed rate, a fixed principal amount, and a fixed compounding cycle, the return is an exponential function of time. Using the formula, , let r = 10%, P = 1, and n = 1 and give the coordinates (t, A) for the points where t = 0, 1, 2, 3, 4. Round your

calculus
the graph (x^515*x^3 +10) is sketched without axes and not to scale. I found f'(x), set it to zero and got x=0, x=3, x=3. these are critical numbers? I plugged them into original equation to find y (?) and got (0,10),3,152)(3, 172). I have to show for

calculus
hi we have been given a graph and we need to fing its equation. the graph is logistic. we are asked to take any six points on it and then apply appropriate log to get a straight line. i don't know how to get that straight line? i just know for exponential

Calculus (pleas help!!!)
Please answer the following questions about the function f(x)=e^(0.5x^2) Instructions: If you are asked to find x or yvalues, enter either a number, a list of numbers separated by commas, or None if there aren't any solutions. Use interval notation if

Calculus
THANK YOU TUTORS SO MUCH FOR YOUR HELP Determine the intervals on which the function is concave up or concave down. I finally understand that when f'' is greater than 0 it means concave up. f(X) = 18x^2 + x^4 so I differentiate that to be 36x + 4x^3 that

ALGEBRA 2 (LOGARITHMIC FUNCTIONS)
These are some I chose to practice but I have a hard time knowing how to do it. The answers are online but that doesn't help. These deal with logarithmic functions etc. PLEASE HELP! THANKYOU 1.)solve the equation: 3^(x+1)=27^(x+3) 2.) e^x=5 3.) 2^(3x)+9=25

math
Given an exponential graph that are concave up and the points (1,4) and (1, 16), give a possible formula of the function. I plugged the variables into the f(x)=b times a^x and got: 4= b times a^1 and 16=b times a^1 I am not sure where to go from here.

Calculus
Given the graph of f'(x) with f(x) continuous on all reals, find the intervals f(x) is concave up and down and find the X values of the points of inflection. I did points 2 concave down to 2 then concave up 4.

Calculus
Identify the open intervals on which the graph of f(x)=3/(x^2+12) is concave up and/or concave down. Please give in interval form.

Math  Simple rational functions (check)
Consider the function f(x) = x/(x1) Are there any turning points? Explain how this could help you graph f(x) for large values of x? Ans: turning points is another word for checking the concavity, and therefore i find the second derivative and equate it to

Please check my Calculus
1. Find the value(s) of c guaranteed by Rolle’s Theorem for f(x)=x^2+3x on [0, 2] A. c=3/2 B. c=0, 3 C. Rolle’s Theorem doesn’t apply as f is not continuous on [0, 2] D. Rolle’s Theorem doesn’t apply as f(0) does not equal f(2) E. None of these

calculus
Use a sign chart to determine the intervals on which f(x)=4x^3x^4 is concave up and concave up and concave down, and identify the locations of any inflection points.

Calculus
Explain the global optimization process for a continuous function over a closed interval. Be sure to identify all steps involved and clearly explain how the derivative is utilized in this process. Would this be a good explanation? The process of global

Calculus
Sketch the graph of f(x)=x+2/x4. Find the vertical and horizontal asymptotes, critical points, concave up/down, and inflection points.

Calculus
For R"(x) = 15[(x1)(e^x)(e^x)] with 0 < x < 7 What interval is the graph concave and and concave down? I know concave up is (0,2). Is that right? Does concave down exist?

Calculus
Can someone explain this question to me? What intervals should I use to test whether or not the graph is concave up or down. I know that no points or equations are given so we have to estimate. Here is the URL for the graph. imgur dotcom/FdQCV

calculus
Let f (x) = x3 ��3x2 +5x+2. Find the open intervals on which f is concave up (down). Then determine the xcoordinates of all inflection points of f . 1. f is concave up on the intervals 2. f is concave down on the intervals 3. The inflection

calculas 2
can someone please explain to me 1. When doing parametric curves how do you find concavity (concave up or concave down) 2. When doing polar coordinates how do you graph them and how to find different polar points that satisfy a condition like theta0 Have

Precalculus
The exponential function f(x)=6(4)^2x+2 can be written in the standard form f(x)=Abx. Find the values of A and b. Give exact values, not decimal approximations. I don't know how to do with this problem. I try to graph and use points but the answer is wrong

Calculus
3. Discuss the graph of y=x/3+2+3/x. Determine the values of x for which the graph is a. Continuous b. Rising c. Falling d. Concave upward e. Concave downward f. Has a relative maximum g. Has a relative minimum

Calculus
Sketch the graph of f(x)=x^4 + 4x^3  16x + 16: Find the critical points, concave up/down, inflection points, vertical asymptotes and horizontal asymptotes.

Calculus
Find the intervals where the function f(x)=((2x1)^2)(x3)^2 is concave up and concave down and find all inflection points. Give decimal answers using two decimal place accuracy. Please help me!!! I really don't understand! and please show your work so

Maths
Let f(x)= x^55x+3 1Find f'(x) and f"(x). 2Find the intervals on which f(x) is increasing or decreasing. 3Find the local maximum and minimum of f(x), if any. 4Find the intervals on which the graph of f(x) is concave up or concave down. 5Find the

Calculus
Let f(x)=−x^4−8^x3+5^x+2. Find the open intervals on which f is concave up (down). Then determine the xcoordinates of all inflection points of f. 1. f is concave up on the intervals 2. f is concave down on the intervals 3. The inflection points occur

college algebra
On the graph, plot all relevant points for y=x^24x+y^22y+8. Then give the equation for a graph that shifts down 1 unit and to the right 2 units. If it is a function, give its domain and range. Thank you!!

calculus
Use a sign chart to determine the intervals on which f(x)=4x^3x^4 is concave up and concave down, and identify the locations of any inflection points.

AP Calculus
For the function y=42x^2+1/6x^4 find the following: Domain x and y intercepts Vertical asymptotes Horizontal asymptotes Symmetry F'(x) Critical numbers Increasing f(x) Decreasing f(x) Extrema F"(x) Possible points of inflection Concave up Concave down

alg 2
Write an exponential function whose graph passes through the given points. 1. (0, 3) and (1, 15) 2. (0, 5) and (3, 135) 3. (0, 0.3) and (5, 9.6)

Calculus
Find the inflection points and where the function is concave up and concave down: f(x)=x/(x+x^2)

Algebra II
Use the equation of the exponential function whose graph passes through the points (0,2) and (2,50) to find the value of y when x= 2. I'm lost!! Thanks.

math
This is a continuous from my last question Let g be a function that is defined for all x, x ≠ 2, such that g(3) = 4 and the derivative of g is g′(x)=(x^2–16)/(x−2) with x ≠ 2. On what intervals is the graph of g concave down? Justify your answer.

math
find the exponential function of the form y=ab^x whose graph passes through the points (4,6) and (7,10) i got a=3.04 and b= 1.185 so my equation is y=3.04(1.185)^4 is this correct? one more problem. find a power function of the form y=ax^b whose graph

Calc
1. Find values of a,b,c, and d such that g(x) = a(x^3)+b(x^2)+cx+d has a local maximum at (2,4) and a local minimum at (0,0) 2. Need someone to explain this. Graph a function f(x) for which: f(3)=f(5)=0 f'(x)4 f"(x)>0 for all x I know there is concave

algebra
a given graph pases through points (18,25) and (19,100) a) compute delta x b) assume graph is linear and find slope c) assume its exponential and find growth factor

college algebra
On the graph, plot all relevant points for y=the absolute value of x1. Then give the equation for a graph that shifts up 3 units and to the left 4 units. If it is a function, give its domain and range. Thank you!!

Calculus
Given the graph of f'(x) with f(x) continuous on all reals, find the intervals f(x) is concave up and down and find the x values of the points of inflection.

college algebra
On the graph, plot all relevant points for y=x^24x+3. Then give the equation for a graph that shifts up 2 units and to the left 3 units. If it is a function, give its domain and range. Thank you!!

Calculus
Suppose f(x)= e^(1/x). Graph this function in the window 5(

Calculus
Suppose f(x)= e^(1/x). Graph this function in the window 5(

increasing decreasing and more
How to analytically find the intervals on which the function y = 2x^4  4x^2 + 1 is 1)increasing 2)decreasing 3)concave up 4)concave down Also find any local extreme values and inflection points. Thanks. (1) The function is increasing when the first

Calc
analaze the graph of y = 2/ (x^29) yintercepts: ____________________ vertical asymptotes: ____________________ horizontal asymptotes: ____________________ increasing intervals: ____________________ decreasing intervals: ____________________ relative

math
could you please explain how to graph two functions on a calculator at the same time? One is linear and one is exponential and I am to graph the at the same time. I put one of them in as y1 and one in as y2, but the only one that shows up is the linear

Calculus check
Help me check my calculus 1. The graph of f '(x) is continuous, positive, and has a relative maximum at x = 0. Which of the following statements must be true? a. The graph of f is always concave down. b.The graph of f is always increasing. c. The graph of

APCalculus
For the function y=42x^2+1/6x^4 find the following: Domain x and y intercepts Vertical asymptotes Horizontal asymptotes Symmetry F'(x) Critical numbers Increasing f(x) Decreasing f(x) Extrema F"(x) Possible points of inflection Concave up Concave down

Algebra
Construct exponential functiom of points (0,200) and (6,380). The exponential function is y(x)=____

Calculus (urgent!!)
Please answer the following questions about the function f(x)=e^(0.5x^2) Instructions: If you are asked to find x or yvalues, enter either a number, a list of numbers separated by commas, or None if there aren't any solutions. Use interval notation if

Calculus (pleas help!!!)
Please answer the following questions about the function f(x)=e^(0.5x^2) Instructions: If you are asked to find x or yvalues, enter either a number, a list of numbers separated by commas, or None if there aren't any solutions. Use interval notation if

College Algebra
Graph the exponential function. f(x)=4^x Clear All Draw: Exponential.

Maths
find the points of intersection of (a) the tangents to the graph of y=2+2xx^2 at the points where the graph meets the xaxis. (b) the normals to the graph at these points. (c) find the area of the triangle created from the two intersections and the point

Calculus rate of change
Can you please check my answers and fix the ones if any that are wrong. Along with help on part d Consider the following fun f(x)=(3/4)x^3 x^33x^2+6x A.find relative extrema and identify max and min. I got x=1 max ,±√2 min B.determine the interval(s)