Product Rule

[jself]

Use the product rule or quotient rule to find the slope of the line tangent to the graph of the function at the given point. Then compare your result visually with the given graph-as a rough check.

The problem is:
f(x)=(x^2-4) (1+2x) at (-1,3)

Here is somewhat what the picture looks like in the book.

 

[galactus]

Differentiate your function:

\(\displaystyle f(x)=(x^{2}-4)(1+2x)=x^{2}+2x^{3}-4-8x\)

\(\displaystyle f'(x)=6x^{2}+2x-8\)

\(\displaystyle 6(-1)^{2}+2(-1)-8=-4\)

\(\displaystyle \L\\y=mx+b\)

\(\displaystyle \L\\3=(-4)(-1)+b\)

b=-1

y=-4x-1