A differentiable function g is defined for all real numbers and satisfies
g′(x)=x2−4x+136x−4,g(0)=5.
Use this information to analyze the behavior of g.
a. Find an explicit expression for g(x). Show all work, including the constant of integration determined by the initial condition.
b. Determine all critical points of g and classify each as a relative maximum, relative minimum, or neither. Support your answer with appropriate reasoning.
c. Compute ∫03g′(x)dx and state its numerical value. Then use the result to find g(3). Explain how your answer is consistent with the net change theorem.