(D) Given the function $y = x^4$.Find the derivative with respect to $x$: $\frac{dy}{dx} = 4x^3$.For the function to be increasing,$\frac{dy}{dx} > 0$

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Increasing in $(0, \infty)$ and decreasing in $(-\infty, 0)$

(D) Given the function $y = x^4$.Find the derivative with respect to $x$: $\frac{dy}{dx} = 4x^3$.For the function to be increasing,$\frac{dy}{dx} > 0$,which implies $4x^3 > 0$,so $x > 0$.Thus,the function is increasing in the interval $(0, \infty)$.For the function to be decreasing,$\frac{dy}{dx} Thus,the function is decreasing in the interval $(-\infty, 0)$.

Class 12 Mathematics Applications of Derivatives Increasing and Decreasing function

Medium

What type of function is $y = x^4$?

A
Strictly increasing
B
Strictly decreasing
C
Decreasing in $(0, \infty)$ and increasing in $(-\infty, 0)$
D
Increasing in $(0, \infty)$ and decreasing in $(-\infty, 0)$

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Applications of Derivatives

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Increasing and Decreasing function

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What type of function is $y = x^4$?

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