QJEEM20Ma2fe5: JEE Main 2020 Mathematics - Class 12 JEEM20Ma2fe5 Solution: The function, f(x) = (3x – 7)x 2/3 , x ∈ R, is increasing for…

Question

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The function, f(x) = (3x – 7)x^2/3, x

\in

R, is increasing for all x lying in :

Accepted Answer

f(x) = (3x – 7)x^2/3

f’(x) =

(3 x - 7) \frac{2}{3 x^{1 / 3}} + x^{\frac{2}{3}} .3

=

\frac{6 x - 14 - 9 x}{3 x^{1 / 3}}

=

\frac{15 x - 14}{3 x^{1 / 3}}

As f(x) increasing so f'(x) > 0

∴

\frac{15 x - 14}{3 x^{1 / 3}}

> 0

∴

x

\in

(- \infty, 0) \cup (\frac{14}{15}, \infty)

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