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(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.$C(x)=x^{1 / 3}(x+4)$

A. $c(x)$ is increasing when $x \in(-1, \infty)$$c(x)$ is decreasing when $x \in(-\infty,-1)$B. Local minimum $=C(-1)=-3$C. $\mathrm{CU} :(-\infty, 0),(2, \infty) \quad \mathrm{CD} :(0,2) \quad$ inflection points $(0,0),(2,6 \sqrt[3]{2})$D. SEE GRAPH

Calculus 1 / AB

Chapter 4

APPLICATIONS OF DIFFERENTIATION

Section 3

Derivatives and the Shapes of Graphs

Derivatives

Differentiation

Applications of the Derivative

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for this question, we need toe right out the narratives for see at the beginning and the second with the narrative. So for Papuan, we want to find the increasing and be Christine Herbal. So he says, See prime to be zero. Also, we have X equals of minus one, but we also need to consider um, the frost majority. It does not exist. So when X equals zero, that's the first solidarity. If that's not exist, that means we need to consider interval from minus infinity to minus one and from minus 20 0 and from zero to infinity over the first interval. See prime this positive. So sits up. See price and active. The function is decreasing over the second hurdle. See promise positive. The function is increasing over the last it Roxy Prime Minister also positive the functions increasing that means for palatable. We have a local lenamon that x the coast of minus one with values see off minus or in Khost of miners green. And for posse, we said to say, for the purity of to be zero. So we have XY closer to again. We need to consider X equals zero, because at this point on the Saco majority of does not exist. So we have to wear three sub intervals from minus infinity to zero from 0 to 2 in the front. Tool to infinity over the first interrupt. See, double prime is positive, so it functions can keep up over the second. Horrible. See, double prints, connective. The functions can keep down over the last interval. Um, the second of narrative is positive. The of the functions come cave up. So in fact, with two inflection points between connection points head, um, X equals zero in the XY quest to Based on this information, we can schedule a graph for faith. It's the first relabeled some the critical point X equals one minus one and X equals zero. And we have an inflection point at zero and two. Okay, so the function is decreasing first, and they it has a local minima taxi Costa minus one on day increasing. So the function we passed this to your point listed minus 40 and the so basically, we have something like this. So when exist, lesson zero, the function is actually come cave, um, his conclave off based on for a second. They're from zero to the FARC is concave down something like it is. And we passed the point to function the country pop again. So the phone function looks actually, So we have to inflection points. So we must change the contribute e. And then we have a local minimum, which is also a global meaning that we can see that and we have two x intercept.

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