(B) Let $f(x) = x^4 - 4x$.To find the interval where the function is decreasing,we find the derivative $f'(x) = 4x^3 - 4$.The function is decreasing w

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(B) Let $f(x) = x^4 - 4x$.To find the interval where the function is decreasing,we find the derivative $f'(x) = 4x^3 - 4$.The function is decreasing when $f'(x) $4x^3 - 4 $4(x^3 - 1) $x^3 Taking the cube root on both sides,we get $x Thus,the function is decreasing in the interval $( - \infty, 1)$.

Class 12 Mathematics Applications of Derivatives Increasing and Decreasing function

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The function $f(x) = x^4 - 4x$ is decreasing in the interval

A
$[-1, 1]$
B
$( - \infty, 1)$
C
$[1, + \infty)$
D
None of these

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Class 12

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Applications of Derivatives

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Increasing and Decreasing function

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The function $f(x) = x^4 - 4x$ is decreasing in the interval

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Find the intervals in which the function $f(x) = (x+1)^{3}(x-3)^{3}$ is strictly increasing or strictly decreasing.

Show that the function given by $f(x) = \sin x$ is decreasing in $\left(\frac{\pi}{2}, \pi\right)$.

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