Question

Consider the function f(x)=x^2−4x+3 on the interval [0,4]. Verify that this function satisfies the three hypotheses of Rolle's Theorem on the interval.
f(x) is _______ on [0,4]
f(x) is _______ on (0,4)
f(0) = f(4)= ?

Then by Rolle's theorem, there exists a c such that f′(c)=0. Find the value c.

Answer 1

The following are the answers to the questions presented:

f(x) is defined on [0,4]

f(x) is continuous on (0,4)

f(0) = f(4)= 3

c= 2

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