Question

Find the critical points of the function f(x)=45x^4/5+x^9/5​

Answer 1

Explanation:

`\mathrm{Critical\:Points\:of}\:45(x^4)/(5)+(x^9)/(5):`
`x=-\sqrt[5]{20},\:x=0`

Critical Point Definition:

• Critical points are points where the function is defined and its derivative is zero or undefined.

Find where
`f'(x)` is equal to zero or undefined

`x=-\sqrt[5]{20},\:x=0`

Identify critical points not in
`f(x)` domain

Domain of
`45(x^4)/(5)+ (x^9)/(5): -{ \infty} < x < { \infty}`

All critical points are in domain

`x=-\sqrt[5]{20},\:x=0`