The table below gives values of a twice- differentiable function f and its first derivative f'...

 

  

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The table below gives values of a twice- differentiable function f and its first derivative f' for selected values of x. Let g be the function defined by g (x) = f (2x – x²). - -3 3 4 f (x) 5 -1 2 7 f' (x) -2 4 1 What is the value of g' (-1) ? (b) It is known that g" (0) = 0. What is the value of f" (0) ? (c) Is there a value c, for 0 <c< 3, such that g (c) = 2 ? Justify your answer. (d) Let h be the function with first derivative given by h' (x) = 4xe" . At what value of x in the interval 0 <x < 4 does the instantaneous rate of change of h equal the average rate of change of f over the interval 0 < x<4? The table below gives values of a twice- differentiable function f and its first derivative f' for selected values of x. Let g be the function defined by g (x) = f (2x – x²). - -3 3 4 f (x) 5 -1 2 7 f' (x) -2 4 1 What is the value of g' (-1) ? (b) It is known that g" (0) = 0. What is the value of f" (0) ? (c) Is there a value c, for 0 <c< 3, such that g (c) = 2 ? Justify your answer. (d) Let h be the function with first derivative given by h' (x) = 4xe" . At what value of x in the interval 0 <x < 4 does the instantaneous rate of change of h equal the average rate of change of f over the interval 0 < x<4?