Find the value(s) of c guaranteed by Rolle's Theorem for f(x)= x^2 +3x on [0,2]

Question

How 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

 

Answer 1

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