Question

83. (a) Show that the symmetric difference quotient \frac{f(x+h)-f(x-h)}{2h} is the slope of the secant line to the graph of \(f\) from \(x-h\) to \(x+h\). (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 \(x\).

          83. (a) Show that the symmetric difference quotient \frac{f(x+h)-f(x-h)}{2h} is the slope of the secant line to the graph of \(f\) from \(x-h\) to \(x+h\). (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 \(x\).

83. (a) Show that the symmetric difference quotient (f(x+h)-f(x-h))/(2h) is the slope of the secant line to the graph of f from x-h to x+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.

Added by Virginia G.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Linda Hand

07/27/2021

Step 1

Step 1: The slope of a secant line to the graph of a function f from x-h to x+h is given by the difference quotient: \[ \frac{f(x+h) - f(x-h)}{(x+h) - (x-h)} \] Show more…

Show all steps

Thanks for your feedback!

slope of the secant line to the graph of f from x-h to x+h.Include an illustration.) b Prove that the symmetric difference quotient is the average of the slopes of the secant lines from x tox+h and from x-h to x.