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

ok so we know that the function is cont. [0,4] because it has no discontinuity on any interval.
f(0)=3 f(4)=3
so f(0)=f(4)=3
so by rolle's theorem, there exists a c such that f′(c)=0 and 0<c<4. let's now find c.
f'(x)=2x-4
so we're finding c where f'(c)=0
f'(c)=0
2c-4=0
c=2 <---answer

Answer 2

but what is f(x) on the intervals [0,4] and (0,4)

Answer 3

it is defined on interval [0,4] and continous on (0,4)

Answer 4

my software doesnt accept that

Answer 5

c=2

Answer 6

it was established that c=2 long time ago

Answer 7

what i am trying to know is what is f(x) on the interval [0,4] and (0,4)