How do you find local maximum value of f using the first and second derivative tests: #1/3(y2)=sin1/2(x90*) #?
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To find the local maximum value of ( f ) using the first and second derivative tests for the function ( \frac{1}{3}(y2) = \sin\left(\frac{1}{2}(x90^\circ)\right) ), follow these steps:
 Find the first derivative ( f'(x) ) by implicitly differentiating the given function with respect to ( x ).
 Set ( f'(x) ) equal to zero and solve for ( x ) to find critical points.
 Find the second derivative ( f''(x) ).
 Evaluate ( f''(x) ) at each critical point found in step 2.
 Use the first and second derivative tests to determine the nature of each critical point and identify local maximum values.
Let's go through the steps:

Implicitly differentiate ( \frac{1}{3}(y2) = \sin\left(\frac{1}{2}(x90^\circ)\right) ) with respect to ( x ) to find ( f'(x) ). [ f'(x) = \frac{d}{dx}\left(\sin\left(\frac{1}{2}(x90^\circ)\right)\right) ]

Set ( f'(x) = 0 ) and solve for ( x ) to find critical points.

Find the second derivative ( f''(x) ). [ f''(x) = \frac{d^2}{dx^2}\left(\sin\left(\frac{1}{2}(x90^\circ)\right)\right) ]

Evaluate ( f''(x) ) at each critical point found in step 2.

Use the first and second derivative tests to determine the nature of each critical point and identify local maximum values.
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When evaluating a onesided 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 onesided 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 onesided 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 onesided 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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