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

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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**

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