Write a function f(x) that has the given characteristics. f(-6) = f(8) = 0; f'(1) = 0; f'(x) < 0 for x < 1; Select the graph that has the given characteristics. f'(x) > 0 for x > 1 Step 1 We want to find a function that has zeros at x = -6 and x = 8. Recall that for a polynomial function f(x), f(c) = 0 if and only if (x - c) is a factor of the polynomial. So we can state that (x-(-6)) and (x - ])) are factors of the function we are seeking. One possible function with the stated zeros is given by the formula below. f(x) = a (x + 6)(x − ( [

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