Function f(x) = x^4 - x^3 3 is - Vidyadip

MCQ

Function $f(x) = {x^4} - {{{x^3}} \over 3}$ is

✓
Increasing for $x > \,{1 \over 4}$ and decreasing for $x < {1 \over 4}$
B
Increasing for every value of $x$
C
Decreasing for every value of $ x$
D
None of these

✓

Answer

Correct option: A.

Increasing for $x > \,{1 \over 4}$ and decreasing for $x < {1 \over 4}$

a
(a) $f(x) = {x^4} - \frac{{{x^3}}}{3} \Rightarrow f'(x) = 4{x^3} - {x^2}$

For increasing $4{x^3} - {x^2} > 0 = {x^2}(4x - 1) > 0$

Therefore, the function is increasing for $x > \frac{1}{4}$

Similarly decreasing for $x < \frac{1}{4}$.

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