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Tangent and normal lines

I have to understand step by step how to navigate Chapter 3.1 Derivatives of Polynomials and Exponential Functions. However, I don't understand how to get a tangent line from a Y=f (x) if x=a, then use that to find f '(a).

I'm given the following:

Find equations of the tangent line and normal line to the curve at the given point.
Y = X^4 + 2e^x (0,2)

Please explain this step by step.

Answer: Tangent Y = 2X + 2
Normal Y = -(1/2)X + 2

Solution Preview

The slope of the tangent line is given by the derivative of y at x=0. Since
y'=4x^3+2e^x
we know ...

Solution Summary

This shows how to find equations of tangent line and normal line to a given curve.

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