Question

Find the equation of the tangent line and normal line to the curve at a given point y=x^4+2e^x

Answer 1

the slope of the line is given by the derivative

m = dy/dx = 4x^3 + 2e^x

using the point slope form of a straight line
y - y1 = m(x - x1) where m is the above and (x1,y1) is the point of contact of the tangent we have

y - y1 = (4x^3 + 2e^x)(x - x1) which is equation of the tangent