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Second Derivatives and Beyond

Second Derivatives and Beyond

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)
f9(x)
f10(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 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?


f is increasing.
f is positive.
f" is increasing.
f" is positive.
Q. Which of the following functions has no concavity?


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