Let f be differentiable on R and h(x) = f(x) − (f(x))2 + (f(x))3 + 3x + 2 cos x, then
Let f be differentiable on R and h(x) = f(x) − (f(x))2 + (f(x))3 + 3x + 2 cos x, then
Option 1 -
h is increasing whenever f is increasing
Option 2 -
h is increasing whenever f is decreasing
Option 3 -
h is decreasing whenever f is decreasing or increasing
Option 4 -
) h is decreasing whenever f is increasing
Asked by Shiksha User
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1 Answer
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Correct Option - 1
Detailed Solution:h' (x) = f' (x) – 2f (x).f' (x) + 3 (f (x)².f' (x)
= f' (x)/3 (f (x) - 1/3)² + 2/9)
∴ h' (x) ≥ 0 ⇔ f' (x) ≥ 0
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