# What are the critical points of #f(t) = e^tsqrt(2-t+t^2)#?

The function

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To find the critical points of ( f(t) = e^{t}\sqrt{2 - t + t^2} ), we need to find where the derivative ( f'(t) ) is zero or undefined.

First, calculate the derivative ( f'(t) ):

[ f'(t) = e^{t}\sqrt{2 - t + t^2} + e^{t}\frac{1}{2\sqrt{2 - t + t^2}}(-1 + 2t) ]

Set ( f'(t) ) to zero and solve for ( t ):

[ e^{t}\sqrt{2 - t + t^2} + e^{t}\frac{1}{2\sqrt{2 - t + t^2}}(-1 + 2t) = 0 ]

After solving this equation, you will find the critical points of ( f(t) ).

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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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