Calculus 1

I know it's hard to draw a graph here, but I just need an explanation of both if possible. I appreciate any help I can get! :)

"Determine whether the following statements are true and give an explanation or counterexample. Explain why or why not, using complete sentences and appropriate terminology correctly. For part a, include a nice graph to support your claim.

a. Consider the graph of the parabola f(x)=x^2. For a>0 and h>0, the secant line through (a,f(a)) and (a+h,f(a+h)) and always has greater slope than the tangent line at (a+f(a)).

b. d/dx (π^5)=5π^4 "

  1. 👍 0
  2. 👎 0
  3. 👁 65
  1. The secant line has slope
    ((a+h)^2 - a^2)/h = (a^2+2ah+h^2-a^2)/h = (2a+h)
    The slope of the tangent line is 2a
    I'm sure you can graph y=x^2, right?

    d/dx π^5 = 0
    because π is a constant
    However,
    d/dx x^5 = 5x^4
    so at x=π, the tangent line has slope 5π^4

  2. Thanks for your help! I mostly struggled with the explanations, but the graphing was fine.

    1. 👍 0
    2. 👎 0

Respond to this Question

First Name

Your Response

Similar Questions

  1. Math

    1. Graph the points A ( -5,0) B ( -4, 3) and C ( 0, -4) A B C D 2. Identify the quadrant in which (3, -6) lies A II B IV C I D III 3. Determine which ordered pair is a solution of y = 2x - 3 A ( -2, 7) B ( 0, 3) C ( -4, -11 D ( 5,

    asked by Justin on March 23, 2017
  2. physics

    Hey can someone help with this. A movie stuntwoman drops from a helicopter that is 30.0 m above the ground and moving with a constant velocity whose components are 10.0 m/s upward and 15.0 m/s horizontal and toward the south. You

    asked by Mel on September 26, 2008
  3. math

    how to graph this y=6x+20 Graph the y-intercept. Show the lines that indicate the use of slope to graph two more points Draw the line representing the graph of the equation

    asked by help please help!!! on March 1, 2012
  4. socials

    for other event in 1960 i want to draw something related with vietnam war but there too much things i not know what to draw i think hard and idea come that maybe i draw TV picture and write beside as caption that Vietnam first war

    asked by Mohammad on December 6, 2011
  5. Trigonometry

    Graph the function y=2sin(x-2pi/3). To draw the graph, plot all x-intercepts, minima and maxima within on period. I need to graph at least 5 points. I have -pi, 0, pi, 2pi, 3pi, and 4pi along the x-axis

    asked by Shelby on March 24, 2014
  1. Calculus

    Set up a Riemann sum to estimate the area under the graph of f(x) = 5x 2 + 2 between x = 0 and x = 1 using 3 subdivisions and left endpoints. Draw the graph and the 3 rectangles

    asked by Rudy on December 5, 2012
  2. math

    In math class, students must randomly draw a card that contains an equation that they must graph on the board. If the cards contain the equations 2y = 4x + 2, x(x + 1) = 0, 2x + y = 0, x = 2y , x2 + 1 = 0, and y - 2x = 0, then

    asked by MELISSA on March 8, 2011
  3. Math

    which of the following graphs could represent a function with the following 3 properties? 1) f(x)>0, for x0 would mean that the graph is above the x axis, and f'(x) is less than or equal to 0 would mean that the slope is negative.

    asked by Hannah on February 26, 2011
  4. math

    On graph paper draw a ray from the origin through the point (-10,-10) then draw a ray from the origin through the point (-10,10). Use a protactor to measure the angle formed by the two rays and write the measure on the graph paper

    asked by noahc on January 15, 2013
  5. math

    On graph paper draw a ray from the origin through the point (-10,-10) then draw a ray from the origin through the point (-10,10). Use a protactor to measure the angle formed by the two rays and write the measure on the graph paper

    asked by noahc on January 15, 2013
  6. math

    The following are the amounts (to the nearest dollar) paid by 25 students for textbooks during the fall term: a. Draw an ordered stem and leaf plot to illustrate the data. b. Construct a grouped frequency table for the data,

    asked by kirk on August 14, 2010

You can view more similar questions or ask a new question.