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A day full of math games & activities. Find one near you.
A day full of math games & activities. Find one near you.
A day full of math games & activities. Find one near you.
Find the number c that satisfies the conclusion of the Mean Value Theorem on the given interval. f(x) = x, [0, 9]
Solution:
According to the Mean Value Theorem,
Suppose y = f(x) is continuous on a closed interval [a, b] and differentiable on the interval’s interior (a, b).
Then there is at least one point c in (a, b) at which
(f(b) - f(a))/(b - a) = f’(c)
Now f(x) = x is continuous in the interval (0, 9)
f’(c) = (f(b) - f(a))/(b - a)
= (f(9) - (f(0))/(9 - 0)
= (9 - 0)/(9 - 0)
= 1
Therefore f’(c) = 1
Since f(x) = x and f’(x) = 1 and hence
f’(c) = 1
Therefore c = 1
Find the number c that satisfies the conclusion of the Mean Value Theorem on the given interval. f(x) = x, [0, 9]
Summary:
The number c that satisfies the conclusion of the Mean Value Theorem on the given interval. f(x) = x, [0, 9] is 1.
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