Find the maximum or minimum value of the function fx 3x2 46

Find the maximum or minimum value of the function. f(x) = 3x2 46

So far we have given f(x) = 3x^2 - 46

First we have to find the critical points.

So we need to find derivative of the function.

Here we use the power rule of derivative. I.e if f(x) = x^n then f\'(x) = nx^(n-1)

So f\'(x) = 6x - 46

Now make f\'(x) = 0 and solve for x.

So 6x - 46 = 0 =====> x = 46/6 ===> x = 23/3

This is the parabola function and since leading term 3x^2 is positive.

It opens downwards. So in this case we get the maximum at x = 23/3

So we plug this value x = 23/3 in the original function f(x) = 3x^2 - 46

So f(23/3) = 3(23/3)^2- 46 = 391/3

So f has maximum(391/3) at x = 23/3.

This is the required answer.