# Calculus

1. On what interval is the function f(x)=x^3-4x^2+5x concave upward?

2. For what values of x dies the graph of f(x)=2x^3-3x^2-6x+87 have a horizontal tangent?

Is there no solution because the equation can't be factored?

3. At what point on the curve y=1+2e^x - 3x is the tangent line parallel to the line 3x-y=5?

1. 👍 0
2. 👎 0
3. 👁 829
1. #1
f' = 3x^2-8x+5
f" = 6x-8
f is concave up when f" > 0

#2
f' = 6x^2-6x-6
maybe it cannot be factored, but since the discriminant is positive, it has real solutions. Use the quadratic formula to find them.

#3 you want the slope to be 3.
y' = 2e^x - 3
so,
2e^x - 3 = 3
2e^x = 6
e^x = 3
x = ln 3
y(ln3) = 1 + 6 - 3ln3 = 7-ln27
So, the tangent line is

y = 3(x-ln3) + 7-ln27

See the graph at

http://www.wolframalpha.com/input/?i=plot+y%3D1%2B2e^x+-+3x%2C+y%3D3%28x-ln3%29+%2B+7-ln27

1. 👍 0
2. 👎 0

## Similar Questions

A continuous function f, defined for all x, has the following properties: 1. f is increasing 2. f is concave down 3. f(13)=3 4. f'(13)=1/4 Sketch a possible graph for f, and use it to answer the following questions about f. A. For

2. ### Calculus

1. Locate the absolute extrema of the function f(x)=cos(pi*x) on the closed interval [0,1/2]. 2. Determine whether Rolle's Theorem applied to the function f(x)=x^2+6x+8 on the closed interval[-4,-2]. If Rolle's Theorem can be

Estimate the instantaneous rate of change of the function f(x) = x ln x at x = 1 and at x = 3. (Use h = 0.1, 0.01, 0.001, 0.0001, and so on. Round your answers to four decimal places.) f '(1) = f '(3) = What do these values

4. ### 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

1. ### Calculus

Consider the function of defined by f(x)=x^3/3-4/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.

2. ### AP Calculous

let f be the function defined by f(x)=3X^5 -5X^3 +2 a) on what interval is f increasing? b) on what interval is the graph of f concave upward? c)Write the equation of each horizontal line tangent to the graph of f

3. ### Calculus

Suppose you know that f(x) is an odd functon on the domain of all real numbers and that the function is concave up on the intervals 0 < x < 3 and 5 < x and concave down on the interval 3 < x < 5. List ALL intervals on which the

f is a function that is differentiable for all reals. The value of f ′(x) is given for several values of x in the table below. The table: x -8,-3,0,3,8 f'(x)-4,-2,0,4,5 If f ′(x) is always increasing, which statement about

1. ### math

Given f(x)=cos(5x)on the closed interval [0,2π/5] Find the open intervals where f is concave down and the open intervals where f is concave up. Express your answers in interval notation with exact values.

2. ### Calculus

F(x) = x^5 ln x A) Find the interval on which f is increasing Find the interval on which f is decreasing B) Find the local minimum value of f C) find the inflection point (x,y) Find the interval in which f is concave up Find the

3. ### Calculus, math

Consider the function below. (If an answer does not exist, enter DNE.) f(x) = e^arctan(7x) I did the problem but I have mistakes on some items. I think the ff. are right: Vertical Asymptote: x = DNE Horizontal Asymptote: y =

4. ### Calculus

1. The function is continuous on the interval [10, 20] with some of its values given in the table above. Estimate the average value of the function with a Left Hand Sum Approximation, using the intervals between those given