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JEE MATHEMATICS MCQ: INCREASING & DECREASING

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Analyzing +4 | -1

Let

f(x)=\int e^x(x-1)(x-2) d x

, then

f(x)

decreases in the interval

View answer and explanation

Correct option: C

(1,2)

Option C (

(1,2)

) is correct because

f(x)

decreases when

f'(x) < 0

, which occurs when

e^x(x-1)(x-2) < 0

, leading to the interval

(1,2)

.

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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

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

f

g

are two increasing functions such that

fog

is defined, then If

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

0 < {b^2} < c

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