Questions.

5. Does the function f(x) = 2x3 + 2x2 - x - 1 ever have a negative slope? If so, where? Explain and justify your answer. [2A, 2C] 6. The total cost, C, in hundreds of dollars, of producing x number of swimming pools can be modelled by the function C(t) = 39.2 (1 -*). a) Determine the marginal cost at a production level of 75 pools. Explain what this means to the manufacturer. [2A, IC] b) What is the domain of C(t)? What is the domain of C'(t)? Explain what these domains mean in the problem. [2C] 7. Pick the correct answer and explain your answer with words: [2] Your sibling states "If you finish homework, you can borrow their car". You know this means, "If you don't finish homework, you cannot borrow their car". Your mathematician friend says, "If fis differentiable at x, f is continuous at x". This means: a. if f is not differentiable at x, f is not continuous at x b. if f is not continuous at x, f is not differentiable at x c. knowing f is not continuous at X, does not give us enough information to deduce anything about whether the derivative of f exists at x