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JEE MATHEMATICS MCQ: INCREASING & DECREASING

1 Easy

1 of 1

Analyzing +4 | -1

For all

x \in(0,1)

View answer and explanation

Correct option: B

\log _e(1+x) < x

Option B (

\log _e(1+x) < x

) is correct because the derivative of

g(x)=\log _e(1+x)-x

is negative for

x \in (0,1)

, implying

g(x) < 0

.

More Questions from INCREASING & DECREASING

Practice All Chapter MCQs →

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)