Thread: calculus inflection, increasing, decreasing

1.On what interval the function f(x)=x/(x^2+1) increasing?

(a)[-1,1](b)[-inf,1] (c) [-1,2] (d) [-inf, 2]

2. find the interval on which the function f(x)=x+cosx 0<=x<=2pi is increasing
(a)(pi/3,5pi/3)
(b)5pi/3,2pi)
(c) (pi/2, 3pi/2)
(d)(0,2pi,)
(e)none
3.
How many pointsof inflection does f(x) =x^3e^(-x) have?
(a)0
(b)1
(c)2
(d)3
(e) none
4. consider the function f(x)=x^2 in interval [0,1/2].According to mean value theorem thre must be a number c in (0,1/2) such that f '(c)is equal to particular value d. what is d?
(a) 3/2
(b)1
(c) 1/2
(d)2
(e) none

Originally Posted by bobby77

4. consider the function f(x)=x^2 in interval [0,1/2].According to mean value theorem thre must be a number c in (0,1/2) such that f '(c)is equal to particular value d. what is d?
(a) 3/2
(b)1
(c) 1/2
(d)2
(e) none

Thus,

Thus that number is

How many pointsof inflection does f(x) =x^3e^(-x) have?

Then,


Thus,

Thus,

Thus,

The quadradic has discriminant,
so it has two solution (non-trivial) thus, in total 3 solutions.
Corresponding to 3 inflections points.

Hello, Bobby!

3. How many points of inflection does have?

. . .

Points of inflection occur where

We have: .
Then: .

We have: .

Hence, the roots are: .
. . and: .

Therefore, there are three inflection points . . . answer (d).