JEE MATHEMATICS MCQ: DIFFERENTIATION

1 Easy

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Analyzing +4 | -1

The range of

a \in R

for which the function

f\left( x \right) = \left( {4a - 3} \right)\left( {x + {{\log }_e}5} \right) + 2\left( {a - 7} \right)\cot \left( {\frac{x}{2}} \right){\sin ^2}\left( {\frac{x}{2}} \right),\,\,x \ne 2n\pi ,\,\,n \in N

has critical points, is:

View answer and explanation

Correct option: A

\left[ { - \frac{4}{3},\,2} \right]

Option A (

\left[ { - \frac{4}{3},\,2} \right]

) is correct because it represents the range of 'a' for which the given function has critical points, derived from the condition -1 <= cos(x) <= 1.

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