February 23, 2017

Homework Help: Calculus

Posted by Madeline on Wednesday, December 19, 2012 at 11:52am.

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)).

View graph here: h t t p : / / a s s e t s . o p e n s t u d y . c o m / u p d a t e s / a t t a c h m e n t s / 5 0 d 1 e f f a e 4 b 0 6 9 a b b b 7 1 0 d 3 9 - b l a d e r u n n e r 1 1 2 2 - 1 3 5 5 9 3 5 7 7 5 8 1 7 - g r a p h . p n g

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].

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