How do you find the local extrema for # (x^2)(e^x) # from [2,4]?
since
we get the Points as above.
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To find the local extrema of ( x^2 \cdot e^{x} ) on the interval [2, 4], you first need to find its critical points. Critical points occur where the derivative of the function is zero or undefined.

Find the derivative of the function: [ f'(x) = 2x \cdot e^{x}  x^2 \cdot e^{x} ]

Set the derivative equal to zero and solve for ( x ): [ 2x \cdot e^{x}  x^2 \cdot e^{x} = 0 ] [ x(2  x) \cdot e^{x} = 0 ]
This gives two critical points: ( x = 0 ) and ( x = 2 ).

Check the endpoints of the interval [2, 4], which are 2 and 4.

Evaluate the function at these critical points and endpoints to find the local extrema.
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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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