I need help please !! f(x)=2x^3−33x^2+60x−2 . List of critical numbers ?

Question

f(x)=2x^3−33x^2+60x−2 . List of critical numbers ?

and then list them (separated by commas) in the box below.

List of critical numbers =

Answer 1

If you are looking for the critical points where f'(x) = 0, the answer is: x = 10,1.

To find critical points using Calculus, we set the derivative of the function, f'(x), to 0.

In this example, f'(x) is 6x^2-66x+60. We get this by using the Power Rule.

Next, we can factor out a 6 from this equation, and we get: 6(x^2-11x+10) = 0.

Now, we factor the x^2-11x+10 equation, which results in: (x-10)(x-1). Putting that back into our equation in the line above, we now have: 6(x-10)(x-1) = 0. Solving for x, we get x = 10 and 1.

Hope that helps!