# How do you find the critical numbers of #e^(-x^2)#?

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graph{e^(-x^2) [-2.433, 2.435, -1.217, 1.216]}

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To find the critical numbers of the function ( e^{-x^2} ), you need to find the points where the derivative is equal to zero or undefined. First, find the derivative of the function using the chain rule. The derivative of ( e^{-x^2} ) with respect to ( x ) is ( -2x e^{-x^2} ). Set this derivative equal to zero and solve for ( x ) to find the critical numbers.

So, ( -2x e^{-x^2} = 0 ). Solving this equation yields ( x = 0 ).

Therefore, the only critical number of ( e^{-x^2} ) is ( 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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