What is the extreme value of g(x)= 3x^2 +5x -12

g(x) = 3x^2 + 5x -12

We need
to find the extreme values.

First we notice that the
coefficient of x^2 is positive, then the function has a minimum
value.

Now we will find the derivatives
zero.

==> g'(x)= 6x + 5 =
0

==> x =
-5/6

==> g(-5/6) = 3(25/36) - 25/6
-12

==> g(-5/6)= ( 75 - 150 -432)/ 36 = -507/36 =
-169/ 12

Then the function has a minimum
value at f(-5/6) = -169/12