Question Video: The Mean Value Theorem | Nagwa Question Video: The Mean Value Theorem | Nagwa

# Question Video: The Mean Value Theorem Mathematics • Higher Education

Does the mean value theorem apply for the function π¦ = 2π₯Β³ β 4π₯ + 7 over the closed interval [0, 5]?

01:03

### Video Transcript

Does the mean value theorem apply for the function π¦ equals two π₯ cubed minus four π₯ plus seven over the closed interval zero to five?

To use the mean value theorem, two things must be true about our function π of π₯. It must be continuous over the closed interval π to π. And it must be differentiable over the open interval π to π. Well, the function two π₯ cubed minus four π₯ plus seven is indeed continuous over the closed interval zero to five. Itβs a simple cubic graph that looks a little like this over our closed interval. And to check for the second condition, weβll see what happens when we do differentiate with respect to π₯. The derivative of two π₯ cubed is three times two π₯ squared. Thatβs six π₯ squared. And the derivative of negative four π₯ is negative four. So we obtain dπ¦ by dπ₯ to be equal to six π₯ squared minus four. This is indeed defined over the open interval zero to five. And we can say yes, the mean value theorem does indeed apply.

## Join Nagwa Classes

Attend live sessions on Nagwa Classes to boost your learning with guidance and advice from an expert teacher!

• Interactive Sessions
• Chat & Messaging
• Realistic Exam Questions