JEE MATHEMATICS MCQ: INCREASING & DECREASING

1 Medium

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Application +4 | -1

f(x)=\frac{a^2-1}{a^2+1} x^3-3 x+2 \log _e 5

is a decreasing function of

x

for all

x \in R

, then the set of possible values of

a

, is

View answer and explanation

Correct option: A

[-1,1]

Option A ([-1,1]) is correct because the function is decreasing when its derivative is negative, which leads to the condition a² - 1 <= 0.

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

x

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a

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

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f

g

fog

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

0 < {b^2} < c

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