Question

Locate the absolute maximum value of the functionon the interval [0, 5].

Answer 1

check if any maxima lies in the interval [0,5] by finding f'(x)=0...after getting maximas and minimas check if f''(x)<0 then its maxima then just put that value of x in the f(x)

Answer 2

f'(x)= 3x^2 -27

Answer 3

when does \(3x^2-27=3(x^2-9)=3(x+3)(x-3)=0\)?

Answer 4

When x=3 and x=-3

Answer 5

Is there even a maximum value of this function?

Answer 6

to find absolute maximum, you need to check at x = 2, x = -3 and boundary points

Answer 7

*x=3

Answer 8

http://www.wolframalpha.com/input/?i=maximize+x%5E3-27x%2Bk+%2C+0%3C%3Dx%3C%3D5

Answer 9

okay so would my answer be k-54?

Answer 10

That is what I got from f(x) at 3

Answer 11

you need to find all the 4 values :
f(3)
f(-3)
f(0)
f(5)

and pick the max value

Answer 12

f(3)= k-54
f(-3)= k+54
f(0)=k
f(5)= 206+k

Answer 13

oh it is k at 0

Answer 14

f(3) : k-54
f(-3) : k - 108
f(0) : k
f(5) : k-10

Answer 15

Okay. It must be f(0)

Answer 16

absolute max = max [f(3), f(-3), f(0), f(5)] = k
yes