The function f satisfies f(0) = 20. The first derivative of f satisfies the inequality 0 ≤ f'(x) ≤ 7 for all x in the closed interval [0, 6]. Selected values of f' are shown in the table above. The...

The function f satisfies f(0) = 20. The first derivative of f satisfies the inequality 0 ≤ f'(x) ≤ 7 for all x in the closed interval [0, 6]. Selected values of f' are shown in the table above. The function f has a continuous second derivative for all real numbers.

(a) Use a midpoint Riemann sum with three subintervals of equal length indicated by the data in the table to approximate the value of f (6).

(b) Determine whether the actual value of f (6) could be 70. Explain your reasoning.

(c) Evaluate (integral sign (4 on top/ 2 on the bottom)) f''(x)dx.

(d) Find lim (x (goes to 0) ) ((f(x)) -(20e^x))/(0.5f(x)-(10))