Find the equation of the tangent line to the curve #y=x^4+2 e^x# at the point #(0,2)#.?
First, find the gradient of the line by using the derivative:
To get the gradient of the tangent, evaluate this at
We know the line must pass through the point:
The slope of the tangent line is the first derivative evaluated at the the given x coordinate; this compels us compute the first derivative:
The slope, m, is the first derivative evaluated at
Use the point slope form of the equation of the line: