If you're seeing this message, it means we're having trouble loading external resources on our website.

If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked.

Main content

Course: Staging content lifeboat > Unit 11

Lesson 5: Test your knowledge
Internal courses
Staging content lifeboat
Calculus staging
Test your knowledge
© 2024 Khan AcademyTerms of usePrivacy PolicyCookie Notice

Skill check: Mean value theorem, L'Hopital, and local linearization

Google Classroom

Problem

Let the function f(x)=x2 be defined on the closed interval [1,5]. For what value of c, c∈(1,5), is the slope of the tangent to the graph of f equal to the slope of the secant line connecting (1,f(1)) and (5,f(5))?
  • Your answer should be
  • an integer, like 6
  • an exact decimal, like 0.75
  • a simplified proper fraction, like 3/5
  • a simplified improper fraction, like 7/4
  • a mixed number, like 1 3/4