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Calculus
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Determine whether Rolle's Theorem can be applied to the function on the given interval; if so, find the value(s) of c guaranteed by the theorem. (Enter your answers as a comma-separated list. If Rolle's Theorem does not apply, enter DNE.)

f(x) = 
x
sqrtx (2 − x) on [0, 2]
c=?

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Related questions

1.
a.
Determine whether Rolle's Theorem can be applied to the function on the given interval; if so, find the value(s) of c guaranteed by the theorem. (Enter your answers as a comma-separated list. If Rolle's Theorem does not apply, enter DNE)
f(x) = ln(2 − sin(x)) on [0, 2π]
b. Determine whether Mean Value Theorem can be applied to the function on the given interval; if so, find the value(s) of c guaranteed by the theorem. (Enter your answers as a comma-separated list. If an answer does not exist, enter DNE.)
f(x) = 9x^3 on [0, 3]
c. Determine whether Mean Value Theorem can be applied to the function on the given interval; if so, find the value(s) of c guaranteed by the theorem. (Enter your answers as a comma-separated list. If an answer does not exist, enter DNE.)
f(x) = xSqrt(x + 1)
on [0, 3]

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