(a) Show that the symmetric difference quotient (a + h) (a h)/2h is the slope of the secant line to the graph of

(a) Show that the symmetric difference quotient ƒ(a + h) − ƒ(a − h)/2h is the slope of the secant line to the graph of ƒ from x = a − h to x = a + h. (Include an illustration.)
(b) Prove that the symmetric difference quotient is the average of the slopes of the secant lines from x to x + h and from x − h to x.