What are the critical points of #f(x) = 3x-arcsin(x)#?
To find critical points, simply derive and find zeroes of the derivative:
Put these three things along and you have
Now we must find its zeroes:
We can easily solve this last equation:
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To find the critical points of ( f(x) = 3x - \arcsin(x) ), we need to find where its derivative is equal to zero or undefined.
( f'(x) = 3 - \frac{1}{\sqrt{1-x^2}} )
Setting ( f'(x) ) equal to zero and solving for ( x ):
( 3 - \frac{1}{\sqrt{1-x^2}} = 0 )
( \frac{1}{\sqrt{1-x^2}} = 3 )
( \sqrt{1-x^2} = \frac{1}{3} )
( 1-x^2 = \frac{1}{9} )
( x^2 = 1 - \frac{1}{9} )
( x^2 = \frac{8}{9} )
( x = \pm \frac{\sqrt{8}}{3} )
Thus, the critical points of ( f(x) = 3x - \arcsin(x) ) are ( x = \frac{\sqrt{8}}{3} ) and ( x = -\frac{\sqrt{8}}{3} ).
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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.
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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