JEE MATHEMATICS MCQ: INCREASING & DECREASING

1 Easy

1 of 1

Analyzing +4 | -1

Let

f

be any function continuous on

[a,\,b]

and twice differentiable on

(a,\,b)

. If for all

x \in \left( {a,\,b} \right),f'\left( x \right) > 0

and

f''\left( x \right) < 0,

then for any

c \in \left( {a,\,b} \right),\frac{{f\left( c \right) - f\left( a \right)}}{{f\left( b \right) - f\left( c \right)}}

is greater than

View answer and explanation

Correct option: C

\frac{{c - a}}{{b - c}}

Option D (

{\pi ^2}

) is correct because it is the result of evaluating the definite integral using properties of definite integrals.

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)