Think you’ve got your head wrapped around **Second Derivatives and Beyond**? Put your knowledge to
the test. Good luck — the Stickman is counting on you!

Q. Which of the following statements is true?

A differentiable function need not be defined everywhere.

A differentiable function need not be continuous.

A differentiable function need not have a derivative.

A differentiable function need not have a second derivative.

Q. Find the second derivative of the function *f*(*x*) = -sin *x*.

Q. Find the second derivative of the function *f* (*x*) = *xln* x.

1

-*x*^{ - 2}

Q. Let *f* (*x*) be a polynomial of degree 20. Which of the following functions has degree 10?

Q. Let *f*(*x*) = cos *x*. Then f^{(99)}(*x*) =

-sin *x*

-cos *x*

sin *x*

cos *x*

Q. Which of the following functions is decreasing and concave up?

Q. Which of the following functions has both *f*' and *f*" positive?

Q. Which of the following functions has a positive first derivative and a negative second derivative?

Q. Assume that *f* and *f*' are differentiable. If *f*' is increasing, then which of the following must be true?

Q. Which of the following functions has no concavity?