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Second Derivatives and Beyond
Second Derivatives and Beyond

Second Derivatives and Beyond: Thinking Critical 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!

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


f' is zero
f' is zero or undefined
f" is zero or undefined
f" changes sign
Q. Which of the following statements about the function is true?


The function f has no critical points.
x = 0 is the only critical point of f.
x = 2 is the only critical point of f.
x = 0 and x = 2 are both critical points of f.
Q. An inflection point of a function f is a point at which


f' is zero
f' is zero or undefined
f" is zero or undefined
f" changes sign
Q. Which of the following statements about the function f(x) = 4( x - 1 ) - 8 is true?


The function f has no inflection points.
x = 1 is the only inflection point of f.
x = 3 is the only inflection point of f.
x = 1 and x = 3 are both inflection points of f.
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?


x = c is a maximum value of f.
A maximum value of f occurs at x = c.
x = c is a minimum value of f.
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?


f has a minimum at x = 2 and a maximum at x = -5.
f has a maximum at x = 2 and a minimum at x = -5.
f has minima at both x = 2 and x = 5
f has maxima at both x = 2 and x = 5
Q. The derivative of the function f is

f'(x) = 4x + 8

Which of the following statements is true?



f has a minimum at x = 2.
f has a maximum at x = 2.
f has a minimum at x = -2.
f has a maximum at x = -2.

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