# F(x) = x/6, derivative

• May 21st 2012, 09:21 AM
ArtemisLux
F(x) = x/6, derivative
I don't know if this is pre-university or university level calculus,
but it would be greatly appreciated if someone could explain the
following problem to me:

Problem:

Let F(x) = x/6

a. Take the derivative of F(x) with respect to x to find a new function f(x).

I think this should be x-6, am I correct?

b. Suppose f(x) is to serve as a probability model; it then should have a surface area
equal to 1 and all its values should be positive.

Suppose also that the domain starts at zero.

What is the upper boundary of this domain?

• May 21st 2012, 12:35 PM
ebaines
Re: F(x) = x/6, derivative
Quote:

Originally Posted by ArtemisLux
Let F(x) = x/6

a. Take the derivative of F(x) with respect to x to find a new function f(x).

I think this should be x-6, am I correct?

No. The equation f(x)=x/6 is a stright line, with slope 1/6. Since the derivative of a function is its slope, this tells you that the derivative of f(x)=x/6 is f'(x) = 1/6.

Quote:

Originally Posted by ArtemisLux
b. Suppose f(x) is to serve as a probability model; it then should have a surface area
equal to 1 and all its values should be positive.

Suppose also that the domain starts at zero.

What is the upper boundary of this domain?

You want to find the value for 'a' where the area between the curve y=x/6 and teh x-axis taken beween x=0 and x=a is equal to 1. If you've learned integrals (or "anti-derivatives") you can integrate y=x/6 and then solve for a point 'a' such that the definite integral between values of x=0 and x=a is equal to 1. But another way is to realize that the line y=x/6 forms a triangle with the x axis, and the area of that triangle it is one half base length tiomes height, or (1/2)xy. Sinc y = x/6, substitute this and solve for (1/2)x(x/6) = 1.