# What are the critical points of #h(x)=lnsqrt(3x-2(x^2))#?

##### 2 Answers

#### Explanation:

Critical points exist when the derivative of the given point is 0 or undefined.

Let's find

Remember the chain rule, power rule, and finding the derivative of

The chain rule states that:

If

The power rule states that

Also,

Therefore,

=>

=>

=>

=>

=>

=>

Now, we want

We have:

=>

We see that

=>

=>

=>

For

=>

When we solve these, we get:

Now, we check whether these

When we plug this in, we see that

However, when

Therefore, the critical point is at

So critical point is at

#### Explanation:

Set the derivative to zero to find critical points. To derive an ln function use this rule:

To derive u to find u' use the general power rule:

So

Now we have u', so plug it into the derivative of ln equation:

Which after some algebra will give you :

Find the zeroes of this to get the x value of the critical point(s) , which is only