JEE MATHEMATICS MCQ: INCREASING & DECREASING

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Let

g\left( x \right) = f\left( x \right) + f'\left( {1 - x} \right)\,and\,f''\left( x \right) < 0,0 \le x \le 1.

. Then

View answer and explanation

Correct option: B

g\left( x \right)

decreases on [0,1]

The correct answer is D (

g(x)

increases on [0,1/2] and decreases on [1/2,1]) because the function g(x) is increasing when its derivative is positive and decreasing when its derivative is negative, and f''(x) < 0 indicates concavity.

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If the function

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

is increasing for all values of

x

, then The set of values of a for which the function

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

is an increasing function on [1,2] is The value of

a

in order that

f(x)=

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

decreases for all real values is given by The function

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

, is If

f

and

g

are two increasing functions such that

fog

is defined, then If

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

and

0 < {b^2} < c

, then in

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