Problem

(a) Find the intervals of increase or decrease. …

04:02

Problem 31 Medium Difficulty

(a) Find the intervals of increase or decrease.
(b) Find the local maximum and minimum values.
(c) Find the intervals of concavity and the inflection points.
(d) Use the inforvation from parts (a)-(c) to sketch the graph. Check your work with a graphing device if you have one.
$F(x)=x \sqrt{6-x}$

Answer

A. increasing: $(-\infty, 4) \quad$ decreasing: $(4,6)$
B. local maximum: $(4,4 \sqrt{2})$
C. No inflection, Because the graph is concave down for all points in the domain.
D. SEE GRAPH

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Calculus 1 / AB

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Chapter 4

APPLICATIONS OF DIFFERENTIATION

Section 3

Derivatives and the Shapes of Graphs

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Video Transcript

for this question, we can ride out if prime in the f travel primary beginning. So for part A, we said have Primakov's to zero. So we have only have one solution. X equals two for I'm not that the domain of f will be so the domino favor he is, um, from negative. Infinity to six. So I only have two intervals to some intervals to consider. So mine from minus infinity to for in the front 4 to 6 over the front. Seen several, if prying, eyes positive. So the function is increasing over the second arrive. Prime is next in for those sort of function is decreasing in the party. Um, because the funds are increasing than decreasing. What? So we have a local mix at X equals toe fall with value F four equals two, four times wrote off to just plugging for into it. So for Passy, we said, if double prime equals zero ah, which means we have X equals to eight, but eight is outside the old man. So we don't conceive that this as, um and the inflection point candidate. So, um, on mine is unique to a six, we can see that if Tebow Prem is always negative So the functions concave downward. So look, funding is done Work on kept on work over the whole door men. And now we can graph such our Kinski age the graph of F Ah, and they looks like So, um you look so we can see the efforts to root which is 06 And then there's, um ah loco Maximum at X equals toe for with value four times wrote of two So the function looks Looks like, um this So this is the sketch of the graph.

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