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Applications of Derivatives

Critical Points

nta_pyq_2024_apr

Grade 12

Question:

The number of critical points of the function $f(x)=(x-2)^{2/3}(2x+1)$ is:

1

2

0

3

Step-by-Step Solution

Key Concept: $f'(x)=\dfrac{2(3x-1)}{3(x-2)^{1/3}}$. Zero at $x=1/3$; undefined at $x=2$.

2 critical points: $x=1/3$ and $x=2$.

Correct Answer: 2