# Calculus 1

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) = sqrt(x), [0,16]

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1. f(0) = 0
f(16) = 4
slope of secant: 1/4

f' = 1/2√x
1/2√x = 1/4
2√x = 4
x = 4
which is in [0,16]

verify at

http://www.wolframalpha.com/input/?i=plot+y%3D%E2%88%9Ax%2C+y+%3D+%281%2F4%29%28x-4%29+%2B+2+for+0+%3C%3D+x+%3C%3D+16

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