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. A critical point of a function *f* is a point at which

Q. Which of the following statements about the function
is true?

The function *f* has no critical points.

Q. An inflection point of a function *f* is a point at which

Q. Which of the following statements about the function *f*(*x*) = 4( *x* - 1 ) - 8 is true?

The function *f* has no inflection points.

Q. A maximum value of a function *f* is

a *y*-value that is bigger than every other value of *f*.

a *y*-value that is bigger than every nearby value of *f*.

an *x*-value at which *f* is bigger than anywhere else.

an *x*-value at which *f* is bigger than anywhere nearby.

Q. How many minima does the function *f*(*x*) = -5cos x have?

none

one

finitely many, but more than one

infinitely many

Q. *x* = *c* is a critical point of the function *f*. The sign of *f*' is negative to the left of *c* and positive to the right of *c*. Which of the following statements is true?

A maximum value of *f* occurs at *x* = *c*.

A minimum value of *f* occurs at *x* = *c*.

Q. *x* = *c* is a critical point of the function *f*. If *f*"(*c*) = 0, which of the following statements is true?

The second derivative test says that a minimum value of *f* occurs at *x* = *c*.

The second derivative test says that a maximum value of *f* occurs at *x* = *c*.

The second derivative test says that neither a minimum nor a maximum value of *f* occurs at *x* = *c*.

The second derivative test says nothing at all about what occurs at *x* = *c*.

Q. If the derivative of a function *f* is *f*'(*x*) = ( *x* - 2 )(*x* + 5), which of the following statements is true?

Q. The derivative of the function *f* is

*f*'(*x*) = 4*x* + 8

Which of the following statements is true?