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## PowerPoint Slideshow about ' The Mean Value Theorem' - talen

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Example If c is the value defined by the Mean Value Theorem, then for on [0, 1], what is the value of c?

Example If c is the value defined by the Mean Value Theorem, then for on [0, 1], what is the value of c?

Example If c is the value defined by the Mean Value Theorem, then for on [0, 1], what is the value of c?

Example If c is the value defined by the Mean Value Theorem, then for on [0, 1], what is the value of c?

Example If c is the value defined by the Mean Value Theorem, then for on [0, 1], what is the value of c?

= 78 mph

Let f be continuous on [a, b] and differentiable on (a, b). Then there exists a point c in

(a, b) such that:

a

c

b

Let f be continuous on [a, b] and differentiable on (a, b). Then there exists a point c in

(a, b) such that:

a

c

b

Let f be continuous on [a, b] and differentiable on (a, b). Then there exists a point c in

(a, b) such that:

a

c

b

Example Check that the hypothesis for the MVT is true for the function on the interval [0.5, 2].

Example Check that the hypothesis for the MVT is true for the function on the interval [0.5, 2].

f(x) is not continuous at x = 0!

Example Check that the hypothesis for the MVT is true for the function on the interval [0.5, 2].

f(x) is not continuous at x = 0!

That’s okay because 0 is not in [0.5, 2]!

Example Check that the hypothesis for the MVT is true for the function on the interval [0.5, 2].

f(x) is not continuous at x = 0!

That’s okay because 0 is not in [0.5, 2]!

f(x) is not differentiable at x = 0, again, that’s okay!

Example If c is the value defined by the Mean Value Theorem, then for on [0, 1], what is the value of c?

Example If c is the value defined by the Mean Value Theorem, then for on [0, 1], what is the value of c?

Example If c is the value defined by the Mean Value Theorem, then for on [0, 1], what is the value of c?

Now solve for x!

Now solve for x!

Now solve for x!

Now find the roots using your calculator!

Now solve for x!

Now find the roots using your calculator!

This the c value of x that satisfies the MVT!

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