JEE MATHEMATICS MCQ: INCREASING & DECREASING

1 Easy

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Analyzing +4 | -1

f(x)=a x^3+b x^2+c x+d

, where

a, b, c

and

d

are real numbers and

3{b^2} < {c^2}

, is an increasing cubic function and

g(x)=a f^{\prime}(x)+b f^{\prime \prime}(x)+c^2

, then

View answer and explanation

Correct option: B

\int_a^x g(t) d t

is an increasing function

Option B is correct because

g(x) > 0

for all

x

which implies that the integral of

g(t)

from

a

x

is an increasing function.

More Questions from INCREASING & DECREASING

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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)