Asked by Anonymous
If the x-intercept of the tangentto the curve y=e^-x is increasing at a rate of 4 units per second, find the rate of change of the y-intercept when the x-intercept is 6 units.
Answers
Answered by
oobleck
the slope of the tangent is -e^-x
The x-intercept is at x+1, so the y-intercept is at f(x) = (x+1)e^-x
f'(x) = e^-x - (x+1)e^-x = -xe^-x
df/dt = -xe^-x dx/dt
So, at (5,e^-5) df/dt = -5(e^-5)(4) = -20/e^5
The x-intercept is at x+1, so the y-intercept is at f(x) = (x+1)e^-x
f'(x) = e^-x - (x+1)e^-x = -xe^-x
df/dt = -xe^-x dx/dt
So, at (5,e^-5) df/dt = -5(e^-5)(4) = -20/e^5