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Second Derivatives and Beyond

Second Derivatives and Beyond

Second Derivatives and Beyond: What's Concave Up? True or False

1. Which of the following statements is true?A differentiable function need not be defined everywhere.
2. Find the second derivative of the function f(x) = -sin x.f"(x) = cos x
3. Find the second derivative of the function f (x) = xln x.ln x + 1
4. Let f (x) be a polynomial of degree 20. Which of the following functions has degree 10?f10(x)
5. Let f(x) = cos x. Then f(99)(x) =-sin x
6. Which of the following functions is decreasing and concave up?
7. Which of the following functions has both f' and f" positive?
8. Which of the following functions has a positive first derivative and a negative second derivative?
9. Assume that f and f' are differentiable. If f' is increasing, then which of the following must be true?f is increasing.
10. Which of the following functions has no concavity?

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