# Thread: Find a formula for the slope of this line.

1. ## Find a formula for the slope of this line.

A line goes through the origin and a point on the curve given below.
y= x^2*e^(-3x)

Find a formula for the slope of this line.

For what value of x is this slope a maximum? Assume x ≥ 0.

What is the maximum value of this slope?

Tyler

2. What part do you need help on exactly?

For the first part they are asking you to find the slope of a line. To do so we need to points. They have given us one point, the origin and you can generalize the other with (x, f(x)). Now we need to know the formula for the slope of this line:

$\displaystyle m=\frac{x^{2}e^{-3x}-0}{x-0}$

$\displaystyle m=xe^{-3x}$

For your second part, they ask you to find for what values of X, will we get the maximum value for the slope of this line. How do you find the maximum (and minimum) of a function? Once you perform the operation, it will LOOK ugly, but you can factor out the ugly and then it will look very pretty.

For part three, once you have figured out the value of X that generates the maximum value of your slope, you simply plug it right back in to your equation for "m".

3. makes sense, thanks.