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

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

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:

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

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To find all critical numbers for the function ( f(x) = (x + 2)^3 \cdot (x - 1)^4 ), you need to first find its derivative, ( f'(x) ). Then, solve for ( x ) where ( f'(x) = 0 ) and where ( f'(x) ) is undefined. These points will be the critical numbers of the function.

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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- How do you determine all values of c that satisfy the conclusion of the mean value theorem on the interval [-1,1] for #f(x) = x(x^2 - x - 2)#?
- Does the function #f(x) = 2x^2 − 5x + 1# satisfy the hypotheses of the Mean Value Theorem on the given interval [0,2]?

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