# How do you find the point of inflexion of y=xe^(-x)+3? Then the inflectional tangent?

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#y=xe^-x+3#

The inflection point would be

The tangent line would then be

Make y''=0 for the inflection point, which would result in x=2.

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To find the point of inflection of ( y = xe^{-x} + 3 ), you first need to find the second derivative of the function. Once you have the second derivative, set it equal to zero and solve for ( x ). The value(s) of ( x ) obtained will give you the x-coordinate(s) of the point(s) of inflection. To find the corresponding y-coordinate(s), substitute the ( x )-value(s) into the original function.

The inflectional tangent at the point of inflection can be found by evaluating the first derivative of the function at the x-coordinate(s) of the point(s) of inflection. The equation of the tangent line can be written using the point-slope form, where the slope is given by the value of the first derivative at the point of inflection and the point is the point of inflection itself.

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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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