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Maths Differentiation and Applications of Derivatives Maxima and Minima Subjective Type

Published by: CGP EDU Academic Team

Published on: August 13, 2026

Find points of local maxima / minima of

(i) f(x) = (2 x – 1)(2 x – 2) 2

(ii) f(x) = x 2 e –x

(iii) f(x) = 3cos 4 x + 10cos 3 x + 6cos 2 x – 3, x ∈ [0, π ]

(iv) f(x) = 2x + 3x 2/3

(v) f(x) =

Text Solution

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The correct answer is:

CHECK THE SOLUTION.

(i) g(t) = (t – 1) (t – 2) 2

g ′ (t) = (3t – 4) (t – 2)

local maxima at x = log 2 and local minima at x = 1

(ii) f ′ (x) = xe –x (2 – x)

⇒ local min at 0, local max at 2

(iii) f ′ (x) = – 3sin2x (2cos x + 1) (cos x + 2)

local max at x = 0,

local min at x = , π

(iv) f ′ (x) =

local maxima at –1 and local minma at 0

(v) local minima at x = ±, 0

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