Question

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Answer 1

Answer:

Given,

differentiate f(x) with respect to x

now, f'(x) = 0

then,

We also know, domain of and ∈ [ -1 1]

∴ find f(x) at x = 1 , -1 and 1/√2

f(1) = (sin⁻¹(1))² + (cos⁻¹(1))² = π²/4 + 0 = π²/4

f(-1) = (sin⁻¹(-1))² + (cos⁻¹(-1))² = π²/4 + π² = 5π²/4

f(1/√2) = (sin⁻¹(1/√2))² + (cos⁻¹(1/√2))² = π²/16 + π²/16 = π²/8

Hence, maximum value of f(x) = 5π²/4

Minimum value of f(x) = π²/8

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