Thursday

August 28, 2014

August 28, 2014

Posted by **Fabian** on Monday, November 26, 2007 at 8:05pm.

- Math Calculus -
**Michael**, Monday, November 26, 2007 at 9:20pmThe MVT states that

If f is continuous on [a,b] and differentiable on (a,b), then there exists a number c on (a,b) such that

f'(c) = [f(b) - f(a)] / b - a

In other words, the instantaneous slope must equal the average slope at some point c. (Your slope from two points will be the same as the slope of the curve at some point.)

The method I use for applying the MVT to find c on an interval is this...

(1) differentiate the function

(2) note differentiability, continuity

(3) find the regular slope (m) of the secant line

(4) set the derivative equal to m

(5) solve for c

For example, "use the MVT to find c on (-2,2) for f(x)=x^3."

(1) f'(x) = 3x^2

(2) Because f(x) is a polynomial, it is differentiable, and therefore, continuous.

(3) m = [f(2) - f(-2)] / 2 - (-2) = (8 + 8) / (2 + 2) = 16 / 4 = 4

(4) f'(c) = 3c^2 from step 1

setting it equal to our slope m=4,

f'(c) = 3c^2 = 4

(5) c^2 = 4/3

c = +-√(4/3) = +- 2/√3

I hope that helps.

**Related Questions**

Calculus - We're learning about different kinds of functions and I don't really ...

Math Grade 12 Advance Functions - I need help understanding equivalent ...

7th grade math - Hi! What is the formula of the volume and surface area of ...

math-calculus - write the following absolute value functions as piecewise ...

math-calculus - write the following absolute value functions as piecewise ...

Math - Mathmate, I really appreciate all your help regarding my composite ...

Pre-Calculus - Operations with Functions write the function below as either a ...

Calculus - Can someone explain the method of implicit differentiation to me. I ...

Calculus - Can someone explain the method of implicit differentiation to me. I ...

math - I'm having some troubles with these. Thanks in advance. If a>0 find ...