Help Requested.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.

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Help Requested.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.

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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].