Consider the following function and point. Find an equation of the tangent line to the graph of the function at the given point.

Question

Consider the following function and point.

f(x)=x^3+x+5; (-2,-5)

Find an equation of the tangent line to the graph of the function at the given point.

y=

Answer 1

First, find the slope by taking the 1st derivative of the function, and evaluating it at x = -2

The tangent line will have this slope and will pass through the given point --- (-2/-5)

Using the slope/intercept format: y = mx + b, where m is the slope and b is the y intercept:

plug in the value of m found in the first step, and then plug in the x and y values in the given point.

Now you can solve for b.