Question

7. Find the intervals in which the function fgiven by f(x) = x®
5, X+0 is
(i) increasing
(ii) decreasing​

Answer 1

SOLUTION

So, first of all let us differentiate the given function in terms of x let f(x)=y

Therefore,we have,

$\frac{dy}{dx} = \frac{d}{dx} f(x) = {x}^{5} \\ = > \frac{d}{dx}f(x) = 5 {x}^{4}$

After differenciation let us consider,

$\frac{d}{dx}f(x) = 0 \\ = > 5 {x}^{4} = 0 \\ = > {x}^{4} = 0 \\ = > x = 0$

Let us differentiate

$\frac{d}{dx} f(x) = \frac{ {d}^{2} }{d {x}^{2} } f(x) = 5 {x}^{4 } \\ = > \frac{ {d}^{2} }{d {x}^{2} } f(x) = 20 {x}^{3} = 20 \times {0}^{3} = |0|$

Therefore the Funtion is decreasing