I need to graph the function s(x)=200x+1500/0.02x^2+5

I cant figure out how to graph this function...I'm used to functions without (/) in it!

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- Jun 5th 2009, 11:46 AMlisa1984wilsonGraphing
I need to graph the function s(x)=200x+1500/0.02x^2+5

I cant figure out how to graph this function...I'm used to functions without (/) in it! - Jun 5th 2009, 12:00 PMAmer
find critical point f'(x)=0 so you can find the increasing and decreasing intervals that may help and find the concavity of the curve you should first find f''(x)=0 after finding the points (critical points,and the points where f''(x)=0 )but them in the coordinates and find the point where the curve intersect x-axes (y=0) and y-axis (x=0) .....

- Jun 5th 2009, 12:04 PMaidan
The / is an operator used for division.

Akin to + for addition and - for subtraction

and * or x for multiplication.

Is you equation this?

$\displaystyle y = 200x + \frac {1500}{0.02 x^2} + 5 $

If yes then a few of the x,y values

y.value x.value

75205 1

19155 2

8398.3 3

2755 10

4192.5 20

Generate the x,y values from you function and then plot the data.

- Jun 5th 2009, 02:39 PMlisa1984wilson
The equation is set up like a big fraction not division

- Jun 5th 2009, 03:08 PMskeeter
next time, use the proper grouping symbols to make your expression clear ...

**s(x) = (200x+1500)/(0.02x^2+5)**

note that the numerator has degree less than the denominator ...

s(x) is asymptotic to y = 0, the x-axis.

s(x) has a single root at x = -7.5 and is negative-valued for x < -7.5 ; positive valued for x > -7.5

y-intercept is (0,300)

since the denominator is always positive, there are no vertical asymptotes or removable discontinuities.

$\displaystyle s'(x) = \frac{-10000(x-10)(x+25)}{(x^2+250)^2}$

at x = 10, s(x) has a relative maximum because s'(x) changes sign from (+) to (-)

at x = -25, s(x) has a relative minimum because s'(x) changes sign from (-) to (+)

s''(x) will tell you about inflection points and concavity.