C2 Differentiation, range of function?

Find the greatest valus of 6x-x². State the range of the function f(x)=6x-x²

is the first part asking me to find the maximum point.

And what does the range mean??

Thanks :smile:

Reply 1

the bear

the first part is asking you to find the y coordinate of the maximum point.

the range is the set of y values which correspond to the function... once you have found the greatest value it is not difficult.

Reply 2

Hi, How are you ?

Original post by the bear

what does the range mean and do, I still don't understand.

Reply 3

AquisM

Original post by Hi, How are you ?

what does the range mean and do, I still don't understand.

The range is, in short, the numbers that one can get out of this function, i.e. the range of numbers that y can take.

Reply 4

Hi, How are you ?

Original post by AquisM

The range is, in short, the numbers that one can get out of this function, i.e. the range of numbers that y can take.

Y can take to do what??

Reply 5

cenxo

The maximum coordinate would be (3,9).
If you're unsure about this check the wolfram graph; http://www.wolframalpha.com/input/?i=6x-x%5E2+maximum

Hope this helps, try to work it out yourself and see what you get.

Reply 6

Smaug123

Original post by Hi, How are you ?

Y can take to do what??

y is the result of the function. So the range is {f(x), x in the domain of f}. Stated differently, if you plugged every possible value of x into f, and noted down every result you got, you'd get the range of f. (Note, of course, that most functions are defined at infinitely many points - for example, x^2 is defined for every real number, and there are infinitely many of them - so in practice you couldn't actually write down every result.)
Alternatively stated, if you draw a graph of y=f(x), the range is all the values of y for which you can draw a horizontal line through (0,y) and the line would hit the curve f(x). So, for example, the range of:
f(x) = x^2 for -1 <= x <= 1
f(x) = 0 for |x| > 1
is [0, 1], where [a, b] means {x such that a <= x <= b}.

Reply 7

TenOfThem

Original post by Hi, How are you ?

Find the greatest valus of 6x-x². State the range of the function f(x)=6x-x²

is the first part asking me to find the maximum point.

And what does the range mean??

Thanks :smile: