how do i find the maximum and minimum points of a function? f(x) 3x^2+6X-10

Question

anonymous · Answer

do i need to use a quadratic formula?

callisto · Answer

re-arrange the quadratic equation into the form f(x) = a(x-h)^2 +k
If a>0, the curve opens upwards => a minimum point, and vice versa
(h,k) is the coordinates of the vertex
In your case,
 f(x) =3x^2+6X-10
       = 3(x^2 +6x) -10
       =3(x^2 + 6x +3^2 - 3^2) -10
       = 3 (x^2 +6x +9) - 3x3x3 -10
       = 3(x+3)^2 - 37
So, can you work out the answer?

mimi_x3 · Answer

You can differentiate; it's easier I suppose.

anonymous · Answer

it was already differentiated from  f(x)=x3+3x^2-10 x

anonymous · Answer

a book i was using said to use a quadratic formula.i remember using a calculator to solve it once,but i cant remember.

callisto · Answer

Then you should out f'(x) =0
and solve the equation
After that, draw a table and see the change of slope 
If its change is like -ve -> +ve , then it is a minimum point, and vice versa

mimi_x3 · Answer

Then set it to zero.
$$3x^2+6x-10=0$$
You can use the quadratic formula if you want.

callisto · Answer

Sorry i didn't know that you have differentiated it.

mimi_x3 · Answer

You can also find the second derivative to determine the nature.