Find the critical numbers for in the interval . If there is more more than one e

Question

Find the critical numbers for in the interval .

If there is more more than one enter them as a comma separated list.   Enter NONE if the if there are no critical points in the interval.

The maximum value of  on the interval is  

The minimum value of  on the interval is

In the last two, your answer should be a comma separated list of  values or the word "none".

Let

Input the interval(s) on which  is increasing.

Input the interval(s) on which  is decreasing.

Find the point(s) at which  achieves a local maximum.

Find the point(s) at which  achieves a local minimum.

Find the intervals on which  is concave up.

Find the intervals on which  is concave down.

Find all inflection points.

Let . Find the open intervals on which  is increasing (decreasing). Then determine the -coordinates of all relative maxima (minima). 1.   is increasing on the intervals 2.   is decreasing on the intervals 3.   The relative maxima of  occur at  = 4.   The relative minima of  occur at  =
Notes: In the first two, your answer should either be a single interval, such as (0,1), a comma separated list of intervals, such as (-inf, 2), (3,4), or the word "none".

In the last two, your answer should be a comma separated list of  values or the word "none".

Let

Input the interval(s) on which  is increasing.

Input the interval(s) on which  is decreasing.

Find the point(s) at which  achieves a local maximum.

Find the point(s) at which  achieves a local minimum.

Find the intervals on which  is concave up.

Find the intervals on which  is concave down.

Find all inflection points.

Explanation / Answer

For the second question

f(x)=-x^2+5x+6

f'(x)=-2x+5

f'(x)=0 => x=5/2 <++++ 5/2 ----->

f has local max at (5/2,49/4)

f is increasing on (-infiny, 5/2]

f is decreasing on [5/2; +infiny)

f''(x)=-2 => concave down from (- infiny, infiny)

f(x)=4x^3 -48x+4

f'(x)=12x^2-48

f'(x)=0 => x=2 <+++++(-2)--------(2)+++++>

x= -2

f has local max at (-2,68)

f has local min at (2,-60)

f is increasing on (-infiny,-2] and [2, infiny)

f is decreasing on [-2,2]

f''(x)=24x

f''(x)=0 => x=0 <-------(0)++++++>

x=0 is inflection point

f is concave up on (0, infiny)

f is concave down on (-infiny,0)

Related Questions

Navigate

• Browse (All)
• Browse F
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.