Posted by **Madeline** on Wednesday, December 19, 2012 at 11:29am.

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].

## Answer this Question

## Related Questions

- Calculus - Let f be a twice-differentiable function defined on the interval -1.2...
- calculus - Consider the function f(x)=65x−cos(x)+2 on the interval 0 less ...
- Calculus - Consider the function f(x)=6x-cos(x)+5 on the interval 0 is less than...
- Math/Calculus - Find k so that the following function is continuous on any ...
- Algebra 2 - Okay so I need help with basically how to find the domain, range, ...
- math - The function f(x)is defined as f(x)={-2x+3: if -2 less than or equal to &...
- algebra - how do you graph the function... f(x)=2^x over the interval -2 is less...
- alg - the viewing window is defined by -3 is less than or equal to x is less ...
- Calculus - Decide if the following function f(x) is differentiable at x=0. Try ...
- Precalculus - let the function g be defined by g(x)=1-5x if the domain of the ...