# What are the critical values, if any, of #f(x)=x^(4/5) (x − 3)^2#?

##### 1 Answer

They are

#### Explanation:

Critical value of

The domain of

So every point at which

Differentiate using the product rule:

# = (4(x-3)^2+10x(x-3))/(5root(5)x)#

# = (2(x-3)[2(x-3)+5x])/(5root(5)x)#

# = (2(x-3)(7x-6))/(5root(5)x)#

The critical values are

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graph{y=x^(4/5)(x-3)^2 [-3.01, 6.857, -0.442, 4.49]}