What are the critical points of #h(x)=lnsqrt(3x-2(x^2))#?
Critical points exist when the derivative of the given point is 0 or undefined.
The chain rule states that:
The power rule states that
Now, we want
We see that
When we solve these, we get:
Now, we check whether these
When we plug this in, we see that
Therefore, the critical point is at
So critical point is at
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:
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