How do you find all critical numbers of the function #f(x)=x^(4/5)(x-4)^2#?
1 Answer
Explanation:
Critical points are points in the domain where the derivative is equal to zero or where the derivative is not defined.
Derivative Equal to Zero:
The derivative can be found by using the power rule and the chain rule.
Now we set this equal to zero:
We get:
Derivative Not Defined:
The only possible case where
Therefore we set
Therefore, the derivative is not defined at
Conclusion
The critical points of this function are