Calculus/calculus

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Expert: - 1/18/2009


Question
Hi,
Can you please help me with this question.
K(x)=(2x^2+4x)e^-x
I need the first, second derivatives, graph, x intercept, and asymptotes.

Answer
The first derivative involves the product rule with
f(x) = (2x²+4x) and g(x) = e^(-x).

The second derivative involves the product rule of two different terms.  One of them is a -K(x) and the other involves (4x+4)e^(-x).
The second is a product rule with f(x) = 4(x+1) and g(x) = e^(-x).

When the first derivative is 0, you get extreme points.
At these points, when the second derivative is positive,
it is a minimum and when the second derivative is negative,
it is a maximum.

When the second derivative is 0, you get and inflection point.

As x goes off to ∞, the e^(-x) would be overpowering, giving the only horizontal assymptote of y=0.

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