# How many critical points does the function #f(x) = (x+2)^5 (x^2-1)^4# have?

Critical points would be that make f '(x) =0

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To find the critical points of ( f(x) = (x+2)^5 (x^2-1)^4 ), we need to find the points where the derivative is zero or undefined. Then, we'll check the values of the function at these points to determine if they are local maxima, minima, or points of inflection.

Taking the derivative of ( f(x) ) with respect to ( x ) and setting it equal to zero, we get:

[ f'(x) = 5(x+2)^4(x^2-1)^4 + 4(x+2)^5(x^2-1)^3(2x) ]

Setting ( f'(x) ) equal to zero and solving for ( x ), we find the critical points.

After solving for the critical points, you'll need to check the second derivative or perform a first derivative test to determine if each critical point is a local maximum, local minimum, or neither.

However, to directly answer your question, the number of critical points isn't explicitly asked for in the problem. But if you're looking for the number of critical points, you'll have to find them by following the steps mentioned above.

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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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