Please, please HELP with this question?

Question

In a big company, the level of electricity consumption of x months is given by the function C(x) = 300(16x – x^2) – 50, x is an element/is a set of (0, 12). For what range is the level of electricity consumption increasing or decreasing?

Answer 1

well...

C(x) is a quadratic function.
Let's get it into the "turning point" form:

C(x) = 300(16x – x²) – 50
C(x) = –300(x² – 16x) – 50
C(x) = –300[(x – 4)² – 16] – 50
C(x) = –300(x – 4)² + 4750

We can now see that this function has a turning point (4, 4750). It is a maximum turning point (because the leading term is – 300x² and therefore the whole graph looks pretty much like the graph of – x²).
Therefore the function is increasing for all values up to 4, it peaks at 4 and decreases from 4 onwards.

Hope his helps.

Answer 2

You need to see the underlying quadratic: y = x(16-x), which has zeros at 0 and 16. The 300 stretches it vertically, and the -50 translates it down 50. But still it increases on the interval (0,8) and decreases on the interval (8,12). You could go to the trouble of finding 1st and 2nd derivatives, but why, when all that information is there in Alg 1?

Answer 3

c(x) = 300(16x-x^2)-50

c(x)/dx = 300(16 -2x) = 0
4800-600x=0
600x=4800
x=8 So at 8 the function changes direction
c(8) = 300(16(8)-8^2)-50 = 19,150
c(0) = -50
c(12) =14,350

so it rises from 0 to 8 then declines from 8-12