Answer the following questions by using number lines if needed. This is a calculus ab questions and mkust be answer step by step. this is about linearization and connecting f' and f" and extrema.

3. The derivative of a function is f'(x) = (3x - 4)2(x + 5). Find: a) Local maximum b) Local minimum f (x) 16 12 f' (x) 0 -7 4 f" (x) -4 7 -10 5. The table above shows the a twice differentiable function, f and specific values of the function. If A(x) = 2f(f(x)), does A have a critical value at x = 2? If so, is it a max, min, or neither? c) Point of inflection 6. The derivative of a function is g'(x) = =x2 - 4x + 3 and the graph of g passes through the point P(-2,4). Find the linearization of g at x = -2, and use it to estimate g(-2.1). Is the value an under or overestimate? 4. The graph of a continuous function's derivative g'(x) is shown below. Using the graph, estimate: 7. Let f be a differentiable function with f(1) = 14, f'(1) = -12, and f"(x) > 0 from (-1,3). Approximate the value of f (1.5) and state whether it's an overestimate or an underestimate. "a) Where g(x) is increasing and decreasing. Justify your answer. b) Find all local extrema of g(x) and state whether they are a min or a max. Justify. c) Find all points of inflection and justify your answers