The number of critical points of the function f(x) = (x

Engineering

Mathematics

Introduction to Determinants

Question

The number of critical points of the function f(x) = (x – 2)^2/3(2x + 1) is

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$f^{'} (x) = \frac{2}{3} (x - 2)^{\frac{- 1}{3}} (2 x + 1) + (x - 2)^{\frac{2}{3}} (2)$

$= \frac{2}{3} (\frac{(2 x + 1) + 3 (x - 2)}{(x - 2)^{\frac{1}{3}}}) = \frac{10 (x - 1)}{3 (x - 2)^{\frac{1}{3}}}$

x = 1, 2 are critical points.

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