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Let f be a twice-differentiable function defined on the interval -1 .2

Let f be a twice-differentiable function defined on the interval l X < 3 .2 with f (l) derivative off, is shown here: x GraN1 of f' = 2. The graph off', the The graph of f' crosses the x-axis at x=-l and x=3 and has a horizontal tangent at x=2. Letg be the function given by a. What is an equation for the line tangent to the graph of g at x=l? b. For l X < 3 .2, explain to your instructor all of the values of x at which ghas a local maximum. Justify your answer. c. The second derivative Ofg is g" X = ef(x) [ (f' + f" X positive, negative, or zero? Justify your answer. d. Find the average rate of change of g', the derivative of g, over the interval [1,3].