JEE MATHEMATICS MCQ: INCREASING & DECREASING

1 Easy

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Analyzing +4 | -1

Let

{\lambda ^*}

be the largest value of

\lambda

for which the function

{f_\lambda }(x) = 4\lambda {x^3} - 36\lambda {x^2} + 36x + 48

is increasing for all

x \in R.

Then

{f_\lambda }^*(1) + {f_\lambda }^*( - 1)

is equal to:

View answer and explanation

Correct option: D

Option D (72) is correct because after finding the largest value of

\lambda

for which the function is increasing, substituting

\lambda^*

into the function and evaluating at x=1 and x=-1 gives a sum of 72.

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)