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STD 12 - 6. Application of derivatives — JEE STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceJEESTD 12 - 6. Application of derivatives4 Marks
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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