# How do you find the stationary points for #f(x)=x^4# ?

There are 2 ways to test for a stationary point, the First Derivative Test and the Second Derivative Test.

The First Derivative Test checks for a sign change in the first derivative: on the left the derivative is negative and on the right the derivative is positive, so this critical point is a minimum.

The Second Derivative Test checks for the sign of the second derivative:

There is no sign, so the second derivative doesn't tell us anything in this case.

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To find the stationary points for ( f(x) = x^4 ), you need to find where the derivative of the function ( f'(x) ) equals zero. Taking the derivative of ( f(x) ), you get ( f'(x) = 4x^3 ). Setting ( f'(x) ) equal to zero and solving for ( x ), you find the stationary points. ( f'(x) = 0 ) implies ( 4x^3 = 0 ), which has a single solution at ( x = 0 ). Therefore, the stationary point for ( f(x) = x^4 ) is at ( x = 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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