WyzAnt.comHow do you solve this and which answer choice is right and why?
a) c= -3/2
b) c= 0,3
c) Rolle's Theorem does not apply as f is not continuous on [0,2]
d) Rolle's Theorem does not apply as f(0) does not equal f(2)
e) none of these
Find the value(s) of c guaranteed by Rolle's Theorem for f(x)= x^2 +3x on [0,2]
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1 Answer
Lana,
This is straight forward based upon the definition of Rolle's Theorm:
"If a real-valued function ƒ is continuous on a closed interval [a, b], differentiable on the open interval (a, b), and ƒ(a) = ƒ(b), then there exists a c in the open interval (a, b) such that f'(c) =0."
The closed interval for f is [0,2]. f(0)= 0 and f(2)= 10. f(a)≠ f(b). f(x) does not meet the conditions of Rolle's Theorem. Answer=d.
Bruce S
