JEE MATHEMATICS MCQ: INCREASING & DECREASING

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Analyzing +4 | -1

Let

f:[0,2] \rightarrow R

be a twice differentiable function such that

f^{\prime \prime}(x)>0

, for all

x \in(0,2)

.If

\phi(x)=f(x)+f(2-x)

, then

\phi

View answer and explanation

Correct option: C

Decreasing on

(0,1)

and increasing on

(1,2)

Option D (If assertion is incorrect, but reason is correct) is correct because the function f(x) is differentiable at x=1, -1, and 0, making the assertion false, while the reason about the differentiability of |x| and |x^2-1| is true.

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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)