JEE MATHEMATICS MCQ: INCREASING & DECREASING

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Analyzing +4 | -1

Let

f(x)=(1-x)^2 \sin ^2 x+x^2

for all

x \in R

, and let

g(x)=\int\limits_{1}^x\left\{\frac{2(t-1)}{t+1}-\log _e t\right\} f(t)\, dt

for all

x \in(1, \infty)

. Then, which of the following is true?

View answer and explanation

Correct option: B

g

is decreasing on

(1, \infty)

The correct answer is that g is decreasing on (1, ∞) because the derivative of g(x) is negative for all x > 1, indicating a decreasing function.

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

x

f\left( x \right) = {x^2} + ax + 1

a

f(x)=

\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)