Show that f '(x) is 0 at least once in the given intervals a f (x) 1 ex (e 1) sin(( 2)x), 0, 1 b f (x) (x 1) tan x x sin x, 0, 1 c f (x) x sin x (x 2) ln x, 1, 2 d f (x) (x 2) sin x ln(x 2), 1, 3 ...

For each part f C a b f exists o ...

Show that f'(x) is 0 at least once in the given intervals. a. f (x) = 1

Question:

Show that f'(x) is 0 at least once in the given intervals.
a. f (x) = 1 − ex + (e − 1) sin((π/2)x), [0, 1]
b. f (x) = (x − 1) tan x + x sin πx, [0, 1]
c. f (x) = x sin πx − (x − 2) ln x, [1, 2]
d. f (x) = (x − 2) sin x ln(x + 2), [−1, 3]