find all values of c in the open interval (a, b) such that f '(c) = 0. (Enter your answers as a comma-separated list.

Question

find all values of c in the open interval (a, b) such that f '(c) = 0.(Enter your answers as a comma-separated list.

f(x) = (x − 3)(x − 8)(x − 9),    [3, 9]

C=?

Please find the answer so I can see it.

Thanks!

Answer 1

f(x) = (x-3)(x-8)(x-9)

= (x^2 -11x +24)(x-9)

= x^3 -20x^2 +123x - 216

f'(x) = 3x^2 -40x -123

f'(c) = 0 = 3c^2 -40c -123

c = 4/6 + or - (1/6)sqr(1600-4(3)(123))

c = about 4.81 and 8.52

c = 4.81, 8.52

or

c= 4.8, 8.5 rounded off to once decimal place

f(x) has 3 x intercepts, 3, 8, and 9

f(x) = 0 when x=3,8 or 9

f'(x) = 0 once between 3 and 8, and once between 8 and 9

f(x) has a relative maximum at x = about 4.81

f(x) has a relative minimum at x= about 8.52