MCQ
Function $f(x) = {x^4} - {{{x^3}} \over 3}$ is
- ✓Increasing for $x > \,{1 \over 4}$ and decreasing for $x < {1 \over 4}$
- BIncreasing for every value of $x$
- CDecreasing for every value of $ x$
- DNone of these
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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$(A)$ $f(x)$ has three real roots if $a > 4$
$(B)$ $f(x)$ has only one real root if $a > 4$
$(C)$ $f(x)$ has three real roots if $a < -4$
$(D)$ $f ( x$ ) has three real roots if $-4 < a < 4$