Methods2024 Exam 2 Section A · Q10CAS active1 mark

Sign change of the derivative and inverse functions

Suppose a function $f: [0, 5] \to R$ and its derivative $f': [0, 5] \to R$ are defined and continuous on their domains. If $f'(2) < 0$ and $f'(4) > 0$ , which one of these statements must be true?

1 mark

f

is strictly decreasing on

[0, 2]

f

does not have an inverse function.C

f

is positive on

[4, 5]

f

has a local minimum at

x = 3

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