Question

apply the mean value theorem to

Answer 1

apply the mean value theorem to f on [0,1] to find all values of c such that f'(x) = (f(b)-f(a))/(b-a) f(x) = x^3

Answer 2

start by finding below :-
f(b)
f(a)
f'(c)

and plug them above

Answer 3

a = 0, b = 1

Answer 4

do i plug for f' or f?

Answer 5

(f(b)-f(a))/(b-a)

Answer 6

so, its f. not f'

Answer 7

so i get 1? c=1?

Answer 8

how ?

Answer 9

f(b) = 1 f(a) = 0
1-0 / 1-0 = 1

Answer 10

f'(c) = (f(b)-f(a))/(b-a)

f'(c) = 1

Answer 11

you still need to find c :)

Answer 12

o.O T_T how would i go about finding c?

Answer 13

f(x) = x^3

f'(x) = ?

Answer 14

3x^2

Answer 15

yes, so, f'(c) = 3c^2

Answer 16

so its 3?

Answer 17

earlier we got,
f'(c) = 1

3c^2 = 1

solve c

Answer 18

sqrt of 1/3?

Answer 19

\(c = \frac{1}{\sqrt{3}}\) is \(\large \color{red}{\checkmark}\)

Answer 20

so there is only 1 value of c here?

Answer 21

because my question says all values T_T so i wanna make sure

Answer 22

yup ! cuz we're looking oly in interval [0, 1]
1/sqrt(3) is the oly c value

Answer 23

thank you very much.

Answer 24

np :)