# How do you find all critical numbers for the function #f(x)= (x + 2)^3*(x -1)^4#?

##### 1 Answer

Alternatively, we can get the same result by using logarithmic differentiation.

#### Explanation:

Remember the basic concept of the logarithm: it is the opposite of exponentiation. That is to say, if:

Then we can use a logarithm to "cancel out" the exponent, bringing it to the front like so:

Now, we don't have to use the natural logarithm (

Okay, so what's the point? Well, according to the rules of logs, if we take the log of both sides:

We can split the multiplication into addition:

And remember, exponents come down to the front:

Now we can take the derivative, making sure to use the chain rule on the left side:

Now just multiply both sides by

And since

Finally, set

We have three solutions:

The last two clearly mean that

Which is a simple equation that yields

So there you have it: same answer, different method. Use which one you feel most comfortable with - that's the beauty of math.