Find the number c that satisfies the conclusion of the Mean Value Theorem on the given interval. (Enter your answers as a comma-
separated list. If an answer does not exist, enter DNE.) f(x) = x , [0, 16]
1 answer:
Answer:
C = 4
Step-by-step explanation:
solution:
f(x) can be differentiated on (0,16)
By mean value theorem
= f(16) = 4
= f(0) = 0
= f(b) - f(a)/b - a
= f(4) - f(0)/ f(16) - f(0)
= f'(c) = 1/2√C
= 1/2√C = 4/16
= 1/2√C = 1/4
= 4 = 2√C
= √C = 4/2
we make c the subject of the formula and also eliminate the square root
= √C = 2
= C = 2²
= C = 4
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