Question

Function f(x) = x¹⁰⁰ + sinx – 1 is increasing for all x ∈ ______.

विकल्प

• [0, 1]

• `[-π/2, π/2]`

• `[-π/2, 1]`

• [–π, π]

Answer 1

Function f(x) = x¹⁰⁰ + sinx – 1 is increasing for all x ∈ [0, 1].

Explanation:

f(x) = x¹⁰⁰ + sinx – 1

Differentiating w.r.t.x, we get

f'(x) = 100x⁹⁹ + cosx – 0

for x ∈ [0, 1]

100x⁹ > 0 and 

cosx > 0

∴ f'(x) > 0

Hence f is increasing