Find the minimum and maximum values of y in 4x 2 + 12xy + 1…

Maths Differentiation and Applications of Derivatives Maxima and Minima Subjective Type

Published on: August 13, 2026

Find the minimum and maximum values of y in 4x 2 + 12xy + 10y 2 – 4y + 3 = 0.

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(2x) 2 + 2.2x . 3y + (3y) 2 + (y – 1) (y – 3) = 0

(2x + 3y) 2 + (y – 1) (y – 3) = 0

x ∈ R

So D ≥ 0

144y 2 – 16 (10y 2 – 4y + 3 ) ≥ 0

16 [ – y 2 + 4y – 3] ≥ 0

y 2 – 4y + 3 ≤ 0

(y – 1) (y – 3) ≤ 0

∴ 1 ≤ y ≤ 3

So y max = 3 and y min = 1

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