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) = 3x − 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.