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What Derivatives Tell us

Authored by Charles Mensah

Mathematics

University

Used 2+ times

What Derivatives Tell us
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10 questions

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1.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

The function f (x) = 3x2 is

(a) increasing on (−∞, 0) and decreasing on (0, ∞).
(b) increasing on (−∞, ∞).
(c) decreasing on (−∞, 0) and increasing on (0, ∞).

2.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

A function f has the property that f ′(x) > 0 on (a, b) and f ′(x) < 0 on (b, c). It follows that

(a) f is continuous on (a, c).
(b) f is increasing on (a, c).
(c) f is decreasing on (b, c).

3.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

A function f has the property that f ′(x) > 0 on (a, b), f ′(x) < 0 on (b, c), and f ′(b) = 0 . It follows that

(a) f has a local maximum at b.
(b) f has a local minimum at b.
(c) f is undefined at b.

4.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

If f ′ is decreasing on an interval I, then

(a) f is decreasing on I.
(b) f is concave down on I.
(c) f is concave up on I.

5.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

If f ′′(c) = 0 , then

(a) an inflection point occurs at x = c.
(b) the concavity of f changes at c.
(c) c is a candidate for the location of an inflection point.

6.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

If f is concave down on an interval I, then

(a) f is decreasing on I.
(b) f ′′(c) < 0 on I.
(c) f is positive on I.

7.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

The function f has the property that f ′(c) = 0 and f ′′(c) > 0 . It follows that

(a) f has a local minimum at x = c.
(b) f has a local maximum at x = c.
(c) f is increasing on an interval containing c.

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