### Home > CALC > Chapter 3 > Lesson 3.4.4 > Problem 3-187

3-187.

HANAH STRIKES AGAIN!

To calculate the slope of a line tangent to*f*(*x*) at*x*=*a*, most graphing calculators use Hanah's method from problem 3-35, formally called the**Symmetric Difference Quotient**, shown below. Homework Help ✎

Use the symmetric difference quotient to find

*f*′(*x*) if*f*(*x*) = 3*x*− 2 .Use this symmetric difference in your graphing calculator to graph

*f*′(*x*) for*f*(*x*) = sin*x*for*h*= 0.001.

Expand the numerator.

Combine like terms.

Factor out an *h*.

Cancel out the *h*.

Evaluate the limit *h*→0.... this is *f* '(*x*).

Graph that on your calculator. Also sketch the derivative function you found in part (a). The sketches should look a lot alike.