Question

Does the function satisfy the hypotheses of the Mean Value Theorem on the given interval?
f(x) = 4x2 − 3x + 2, [0, 2]

Answer 1

whats the hypothesis of MVT ?

Answer 2

Do you know what the mean value theorem is?

Answer 3

kinda

Answer 4

im trying to know what it is. since f(x) is a polynomial then it is continuous [0,2] and differentiable (0,2)

Answer 5

You have to prove that there exists a "c" in the interval (0,2) such that:
f'(c) = { f(2) - f(0) } / { 2 - 0 }

Answer 6

Well it tells us it's continuous of [a,b], and it's differentiable on (a,b).

Answer 7

on*

Answer 8

ok and then i get five and set it equal to f'x

Answer 9

8/8 =1 cool ok how about this one

Answer 10

Does the function satisfy the hypotheses of the Mean Value Theorem on the given interval?
f(x) = ln x, [1, 6]

Answer 11

between one and 6 its continuous differentiable between (1,6)

Answer 12

\[f'(c) = \frac{ f(b)-f(a) }{ b-a }\]

Answer 13

so F(6)-f(1)/6-1

Answer 14

cool thanks

Answer 15

wait a sec, the question is about testing the hypothesis,
not about finding the solutions right ?

Answer 16

Yeah, for this question it would be sufficient to prove f(x) is continuous in [a,b] and differentiable in (a,b).

Answer 17

i suck at epsilon-delta proofs lol, guess i would just put this argument :

f(x) = 4x2 − 3x + 2, [0, 2]

Since f(x) is a polynomial and since all polynomials are continuous and differentiable everywhere, f(x) satisfies the hypothesis of MVT.

Answer 18

You need to find "c" only if the question asks if the function satisfies MVT.
Here it only asks if it satisfies the hypothesis of MVT.