Find the minimum value fo the function f(x) = 3x^2 + 5x -3

f(x) = 3x^2 + 5x -3

To find
the minimum value , first we identify the sign of x^2, since the sign if positive, that
means the function has a minimum value.

First we will
calculte the critical values of the function which are the first derivative's
zeros.

==> f'(x) = 6x +
5

==> 6x + 5=
0

==> 6x =
-5

==> x= -5/6

Now we
know that the function has a minimum values at x= -5/6

To
find the value we will substitute in f(x);

==>
f(-5/6) = 3*(-5/6)^2 + 5(-5/6) - 3

                 =
3*25/36 - 25/6 - 3

                  = (75 - 150 -
108)/36

                 = -183/36 =
-5.08

Then the function has a minimum value
at f(-5/6) = -5.08