Verify that the function satisfies the three hypotheses of Rolle's Theorem on the given interval. Then find all numbers c that satisfy the conclusion of Rolle's Theorem.
f(x)= x sqrt(x+21) , [-21,0]
If there is more than one solution separate your answers with commas.
c =
Do you know what Rolle's Theorem says?
Rolle's theorem states that if a function f is continuous on a closed interval [a,b] and f(a) = f(b) then
f'(c) = 0 where a <= c <+ b
it is easy to see that f(-21) = -21√0 = 0
and f(0) = 0
f'(x) = (x/2+1)(x+21)^(-1/2)
setting this equal to zero and solving I got x=-2, wich lies between -21 and 0
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