Calculus c

Let f be a twice-differentiable function defined on the interval -1.2 less than or equal to x less than or equal to 3.2 with f(1)=2. The graph of f', the derivative of f, is shown on the right. The graph of f' crosses the x-axis at x=-1 and x=3 and has a horizontal tangent at x=2. Let g be the function given by g(x)=e^(f(x)). 1. Write an equation for the line tangent to the graph of g at x=1. 2. For -1.2 is less than or equal to x is less than or equal to 3.2, find all values of x at which g has a local maximum. Justify your answer. 3. The second derivative of g is g''(x)=x^(f(x)) [(f'(x))^2 + f''(x)]. Is g''(-1) positive, negative, or zero? Justify your answer. 4. Find the average rate of change of g', the derivative of g, over the interval [1,3].

  1. 👍 0
  2. 👎 0
  3. 👁 324

Respond to this Question

First Name

Your Response

Similar Questions

  1. Calculus AP

    f is a differentiable function on the interval [0, 1] and g(x) = f(2x). The table below gives values of f ′(x). What is the value of g ′(0.1)? x 0.1 0.2 0.3 0.4 0.5 f ′(x) 1 2 3 –4 5 The answers are: 1 2 4 cannot be

    asked by Anon on May 1, 2018
  2. calculus

    Let f be a differentiable function such that f(4)=7 and f′(4)=15. The graph of f is concave up on the interval (3,5). Which of the following is true about the approximation for f(3.5) found using the line tangent to the graph of

    asked by toan on January 22, 2020
  3. Calculus

    Rolle's theorem cannot be applied t the function f(x)= ln(x+2) on the interval [-1,2] because a) f is not differentiable on the interval [-1,2] b) f(-1)≠ f(2) c) All of these d) Rolle's theorem can be applied to f(x)= ln(x+2) on

    asked by Mary PLEASEEE on December 19, 2018
  4. Math

    The twice–differentiable function f is defined for all real numbers and satisfies the following conditions: f(0)=3 f′(0)=5 f″(0)=7 a)The function g is given by g(x)=e^ax+f(x) for all real numbers, where a is a constant. Find

    asked by Steven on December 29, 2014
  5. calculus

    If f(x) is differentiable for the closed interval [-3, 2] such that f(-3) = 4 and f(2) = 4, then there exists a value c, -3 < c < 2 such that (4 points) If f(x) = ι(x2 - 8)ι, how many numbers in the interval 0 ≤ x ≤ 2.5

    asked by calc on January 16, 2015
  1. math

    if a and b are the roots of the equation x^2-3x+1=0, what is the value of (1/a) + (1/b)? If the function f is defined by f(x) = (x-1)^2 -3, where -1 is less than or equal to x and 3 is greater than or equal to x. Which of the

    asked by MATH on July 22, 2019
  2. Math - PreCalc (12th Grade)

    The function f(x) = 2x + 1 is defined over the interval [2, 5]. If the interval is divided into n equal parts, what is the value of the function at the right endpoint of the kth rectangle? A) 2+3k/n B) 4+3k/n C) 4+6k/n D) 5+6k/n

    asked by Shawna on March 21, 2014
  3. Calculus

    Determine whether Rolle's Theorem can be applied to f on the closed interval [a,b]. If Rolle's Theorem can be applied, find all values of c in the open interval (a,b) such that f'(x)=0. f(x) = x^(2/3) - 1 [-8,8] I plugged in both

    asked by Maddie on September 26, 2013
  4. Calculus Please Check my answers

    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

    asked by Ke$ha on May 22, 2017
  5. Calculus

    Decide if the following function f(x) is differentiable at x=0. Try zooming in on a graphing calculator, or calculating the derivative f'(0) from the definition. f(x) = x^4sin(2/x), if x is not equal to 0, and f(x) = 0 if x = 0.

    asked by Abigail on February 23, 2011
  6. Calculus

    f is a differentiable function on the interval [0, 1] and g(x) = f(2x). The table below gives values of f '(x). What is the value of g '(0.1) x| .1 .2 .3 .4 .5 f'(x)| 1 2 3 -4 5 So I know f(x) would be the integral of f'(x) which

    asked by Anonymous on May 1, 2018

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