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CGP EDU Academic Team
Published on: August 14, 2026
The function y = f(x) is represented parametrically by
x = t 5 – 5t 3 – 20t + 7 and y = 4t 3 – 3t 2 – 18t + 3, (–2 < t < 2). The minimum of y = f(x) occurs at
Text Solution
Verified by ExpertsThe correct answer is:
D
x = φ (t) = t 5 – 5t 3 – 20t + 7
= φ '(t) = 5t 4 – 15 t 2 – 20 = 5(t 2 – 4) (t 2 + 1) ≠ 0
If – 2 < t < 2
y = ψ (t) = 4t 3 – 3t 2 – 18t + 3
= ψ '(t) = 12 t 2 – 6t – 18
= 0 ⇒ t = – 1 or 3/2
= ψ "(t) = 24t – 6 = ψ "(–1) = – 30
and ψ "(3/2) = 30
y = f(x) is minimum at t = 3/2
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