Second Derivatives and Beyond: What's Concave Up? Quiz
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.
f "(x) = sin x
f "(x) = -sin x
f "(x) = cos x
f "(x) = -cos x
Q. Find the second derivative of the function f (x) = xln x.
1
-x^{ - 2}
ln x + 1
Q. Let f (x) be a polynomial of degree 20. Which of the following functions has degree 10?
f ^{(2)}(x)
f ^{(9)}(x)
f ^{(10)}(x)
f ^{(11)}(x)
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 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?
f is increasing.
f is positive.
f " is increasing.
f " is positive.
Q. Which of the following functions has no concavity?