Graphically:

Plug the equation into your TI-83 calculator and graph.

Use the minimum feature under the calculate menu.

http://mathbits.com/MathBits/TISection/General/BasicGraphing.htm

Differentiation:

Take the first derivative of the equation.

f'(x) = (7x^2)/2 – 1/2x – 1 = 7x – (1/2)

Set the equation equal to zero and solve for x:

7x – 1/2 = 0

7x = 1/2

x = 1/14

Now, plug the 1/14 into your first equation:

f(x) = (7x^2)/2 – x/2 – 1

f(x) = (7(1/14)^2)/2 – (1/14)/2 – 1

f(x) = (7/196) – 1/28 – 1

f(x) = -57/56

The values for the minimum are:

(1/14, -57/56) or (.071428, -1.01786)

Good luck in your studies,

~ Mitch ~

P.S. – When asking a question such as this,

let the reader know which class you’re in.

I can’t tell if you’re in pre-calc, calculus or advanced algebra.