f(x)=x^3-4x^2+2, which of the following statements are true: (1) Increasing in (-infty, 0), decreasing in (83, +infty). (2) Increasing in both (-infty, 0), and (83, +infty). (3) decreasing in both (-infty, 0), and (83,+infty). (4) Decreasing in (-infty, 0), Increasing in (83, +infty). (5) None of the above.

solvarmedw

solvarmedw

Answered question

2022-10-02

Increasing and decreasing intervals of a function
f ( x ) = x 3 4 x 2 + 2, which of the following statements are true:
(1) Increasing in ( , 0 ), decreasing in ( 8 3 , + ).
(2) Increasing in both ( , 0 ), decreasing in ( 8 3 , + ).
(3) decreasing in both ( , 0 ), and ( 8 3 , + ).
(4) Decreasing in ( , 0 ), Increasing in ( 8 3 , + ).
(5) None of the above.
f ( x ) = 0 = 3 x 2 8 x = 0 x = 8 3 , x = 0 are the singular point/point of inflection.Could anyone tell me what next?

Answer & Explanation

Paige Paul

Paige Paul

Beginner2022-10-03Added 11 answers

Step 1
So, when you put f ( x ) = 0 and got x = 0 , 8 / 3, it means that function takes the “u-turn” at those points. Now, we need to check what was happening before x = 0, what’s happening between 0 and 8/3 and what will happen after x = 8 / 3.
We can take any two x’s such that x < 0 and we will find that if x 1 < x 2 then f ( x 1 ) < f ( x 2 ) or we can see that f ( x ) = 3 x 2 8 x is positive for any x < 0 and hence function is increasing in the interval ( , 0 ].
Step 2
And as we know that the function will take a “u-turn” at x = 0 so, the function will decrease between 0 and 8/3 and again after a “u-turn” at x = 8 / 3 it will increase. If you find this “u-turn” concept informal you can go for similar method above and, you will find that f is decreasing between x = 0 and x = 8 / 3, and finally it is increasing for x > 8 / 3

Do you have a similar question?

Recalculate according to your conditions!

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?