How do you find the slope of a parabola y=(1/100)x^2 for a neg. value of x???

Question

I have been toiling over this for a while...*how* do you find the slope of a negative value for x in the graph of the parabola y = (1/100)x^2??

As an example, could you guys give me an explanation as to **how** you would get the answer for the point (-100, 100)???

Awesome i got it, ty all :D

BUT! If someone can help with this...the second part of this problem requires me to find a point on the parabola in which its *tangent* line will intersect (50, 100)! Can anyone figure this out!?!?

Answer 1

As has been said, the derivative dy/dx of x^n = nx^(n-1),
also, if a is a numeric constant, then
d(ay)/dx = (a)[da(y)/dx,
so d[(1/100)(x^2)/dx = (1/100)[d(x^2)/dx = (2)(1/100)x = x/50

The first derivative gives the slope at any point along the curve. So plug in whatever value of x to get the value of the slope at any particular point.

There are a number of derivatives you ought to know. This is one of them. And are a lot you'll become nauseatingly familiar through use. But, there are some reference books you can get that have just about everything you'll ever need to know in math (at least through your Bachelors degree)

A couple I use:
Mathematical Tables from Handbook of Chemistry and Physics, Tenth Edition; Hodgman, Selby, Weast; Chemical Rubber Publishing Co. Cleveland, OH, 1958

Stadard Mathematical Tables, Twelfth Edition; Selby; Chemical Rubber Publishing Co. Cleveland, OH, 1972.

Got the first when I was in College, and the second, I think I got that one because I couldn't find the first one.

Answer 2

The slope part has been answered. This is a parabola. To get the answer for -100,
dy/dx=2x/100=x/50 = -100/50=-2
and for x=100, x/50 = 100/50 = 2

Answer 3

slope of a function at a given point is the 1st derivative.
d(x²/100)/dx = 2x/100 = x/50
so when x = -100, slope is -2.

Answer 4

You take the derivative:

dy = (2/100)x

Then supply the desired x:

dy(-100) = -2

Answer 5

dy/dx = 1/50x
At the point x = -100
dy/dx = -100/50 = -2

slope is -2