I was wondering how to find the x and the y intercepts of the following equation
y = xe^(-x^2/2)
I know for a fact that the intercept is through 0,0 but I don't know how to do this long hand.
When x is zero, y is zero, and vice versa.
To find the x-intercept (where the graph crosses the x-axis) of the equation y = xe^(-x^2/2), we set y to zero and solve for x.
Let's set y = 0 and solve for x:
0 = xe^(-x^2/2)
Since anything raised to the power of 0 is 1, we can divide both sides of the equation by e^(-x^2/2):
0 = x
So the x-intercept is x = 0. This verifies what you mentioned, that the intercept is through (0,0).
To find the y-intercept (where the graph crosses the y-axis), we set x to zero and calculate the corresponding value of y.
Let's set x = 0:
y = 0*e^(0) = 0
Therefore, the y-intercept is y = 0.
In conclusion, the intercepts of the equation y = xe^(-x^2/2) are x = 0 and y = 0.