Question

f(x) = cos(x - 4) - 8

what is the maximum value that this function takes?

Answer 1

The negative 4 shifts it to the right 4 and the -8 shifts it down 8. So you would have the maximum value(since cos(x) normally goes to 1). Of 1-8=-7

Answer 2

f'(x)=-sin(x-4)
-sin(x-4)=0
sin(x-4)=0
remember sin0=0, sinpi=0, and the rest is repeats
x-4=0 => x=4
x-4=pi => x=pi+4
but x=4 and x=pi+4 is for time around a circle (we can keep going around the circle over and over and till foreverness ends)
x=4+2npi
and
x=pi+4+2npi
for n=0,1,2,3,4,5,...
now
f(4)=cos(4-4)-8=cos(0)-8=1-8=-7
f(pi+4)=cos(pi+4-4)-8=cos(pi)-8=-1-8=-9 so since -9<-7 then
the minimum value would be -9
and the maximum value would be -7
the minumums occur at x=pi+4+2npi
maximums occur at x=4+2npi

Answer 3

the options that i have, are: a) 2 b)4 c)8 d)12
so, i dont know ... :/

Answer 4

the word value means the y value
the function is below the x-axis
it is impossible for f to take on any of those y-values

Answer 5

was what i thought.. thank you (:

Answer 6

if they said maximum, then it would be x=4
but they said value

Answer 7

but like i said above there are infinity many maximums