# How do you find the relative extrema for #f(x)=x^4# ?

To find the extrema of a function, just evaluate its derivative and see where it equals zero.

In this case, we have

using the rule

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To find the relative extrema for ( f(x) = x^4 ), you need to find the critical points by setting the derivative equal to zero and then test those points using the second derivative test. The first derivative is ( f'(x) = 4x^3 ). Setting it equal to zero gives ( x = 0 ) as the critical point. The second derivative is ( f''(x) = 12x^2 ). Evaluating the second derivative at ( x = 0 ), we get ( f''(0) = 0 ). Since the second derivative test is inconclusive, we can examine the behavior of the function around ( x = 0 ). The function has a relative minimum at ( x = 0 ) because it changes from decreasing to increasing at that point. Therefore, the relative minimum is ( (0,0) ).

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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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