JEE MATHEMATICS MCQ: INCREASING & DECREASING

1 Easy

1 of 1

Analyzing +4 | -1

Let

f(x)=\left\{\begin{array}{ll}x e^{a x}, & x \leq 0 \\ x+a x^2-x^3, & x > 0\end{array}\right.

where

a

is a positive constant. Then, the interval in which

f^{\prime}(x)

is increasing, is

View answer and explanation

Correct option: C

(-2 / a, a / 3)

Option C ((-2 / a, a / 3)) is correct because it represents the interval where the second derivative of

f(x)

is positive, ensuring that

f'(x)

is increasing.

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f\left( x \right) = \frac{{K\sin x + 2\cos x}}{{\sin x + \cos x}}

x

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\sin x-\cos x-a x+b

f(x)=x e^{x(1-x)}, x \in R

f

g

fog

f\left( x \right) = {x^3} + b{x^2} + cx + d

0 < {b^2} < c

\left( { - \infty ,\;\infty } \right)