Question 1

For f(x) = x² − 6x + 8, which interval is correct?

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Question 2

f(x) = 3x² − 12x + 5. On which interval is f decreasing?

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Question 3

f(x) = −2x² + 8x. Find where f is increasing.

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Question 4

If f'(3) = −5, what can you conclude about f near x = 3?

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Question 5

If f'(x) > 0 on (2, 5), what can you say about f on that interval?

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Question 6

A function satisfies f'(x) = (x−1)(x−4). State the values of x where f has a stationary point.

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Question 7

f(x) = −x² + 4x. For what values of x is f increasing?

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Question 8

The velocity of a particle is v(t) = t² − 6t + 5.

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Question 9

The population P(t) = 500 + 60t − 3t² models a town.

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Question 10

Determine whether h(x) = x³ + 2 is ever decreasing. Justify your answer.

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Question 11

The value of an investment V(t) = 1000 + 200t − 10t² (in dollars, t in years).

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Question 12

g(x) = x³ − 6x. Show that g is decreasing on (−√2, √2).

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Question 13

f(x) = x³ − 3x² − 9x. Find the intervals where f is increasing.

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Question 14

f(x) = x⁴ − 8x². Find all intervals where f is decreasing.

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Question 15

f(x) = 2x³ − 9x² + 12x. Show that f is always increasing for x < 1 and x > 2, and decreasing for 1 < x < 2.

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Topic 5.2: Tangent and Normal Lines Questions

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