Continuing to Payment will take you to apayment page

Purchasing
SparkNotes PLUS
for a group?

Get Annual Plans at a discount when you buy 2 or more!

Price

$24.99$18.74/subscription + tax

Subtotal $37.48 + tax

Save 25%
on 2-49 accounts

Save 30%
on 50-99 accounts

Want 100 or more?
Contact us
for a customized plan.

Your Plan

Payment Details

Payment Details

Payment Summary

SparkNotes Plus

You'll be billed after your free trial ends.

7-Day Free Trial

Not Applicable

Renews March 31, 2023March 24, 2023

Discounts (applied to next billing)

DUE NOW

US $0.00

SNPLUSROCKS20 | 20%Discount

This is not a valid promo code.

Discount Code(one code per order)

SparkNotes Plus subscription is $4.99/month or $24.99/year as selected above. The free trial period is the first 7 days of your subscription. TO CANCEL YOUR SUBSCRIPTION AND AVOID BEING CHARGED, YOU MUST CANCEL BEFORE THE END OF THE FREE TRIAL PERIOD. You may cancel your subscription on your Subscription and Billing page or contact Customer Support at custserv@bn.com. Your subscription will continue automatically once the free trial period is over. Free trial is available to new customers only.

Choose Your Plan

Your Free Trial Starts Now!

For the next 7 days, you'll have access to awesome PLUS stuff like AP English test prep, No Fear Shakespeare translations and audio, a note-taking tool, personalized dashboard, & much more!

Thank You!

You’ve successfully purchased a group discount. Your group members can use the joining link below to redeem their group membership. You'll also receive an email with the link.

Connect any two points, (a, f (a)) and (b, f (b)), on a differentiable
function f to form a line:

Intuitively, it should be clear that we can find a point c between a and b where the
tangent line is parallel to the secant drawn between a and b. In other words, it
should be possible to find a point such that the slope of the tangent at c is the same as
the slope of the secant line drawn from a to b.

This intuitive idea is stated as the Mean Value Theorem, which states that if
f is continuous on [a, b] and differentiable on (a, b), then there exists a point c
on [a, b] for which

f'(c) =

Rolle's Theorem

Rolle's theorem is a special case of the mean value theorem in which f (a) = f (b). It
says: if f is continuous on [a,b] and differentiable on (a,b), and f (a) = f (b), then there is a
c on (a, b) where f'(c) = 0.

The figure below should make clear that this is just a special case of the mean value
theorem: