Given -
y = e^-4t
To Find -
The equation of the tangent =?
Step-by-Step Explanation -
y = e^-4t
So, dy/dx =
y' = -4e^-4t
also,
m = y'(0) = -4e^-4(0)
= -4
So,
when x = 0, y = e^0 = 1
So, point of tangency is (0,1)
Slope of tangent is -4
Using point-slope form:
y - 1 = -4(x - 0)
y = -4x +1
Final Answer -
The equation of the tangent =
y = -4x +1 or at x = t
y = -4t +1