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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 information 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

Calculus 2 / BC

Chapter 4

Applications of Differentiation

Section 3

How Derivatives Affect the Shape of a Graph

Derivatives

Differentiation

Volume

Campbell University

University of Nottingham

Idaho State University

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he is clear. So when you raid here, So for part A, we're gonna find the derivative of C of X, and we get for X plus four over three X to the 2/3 so we're gonna find when it's increasing and decreasing. It's increasing when the derivative is bigger than zero and decreasing when a smaller than zero. So we see that it is increasing when exes between one negative one and infinity and increasing when it's between decreasing. When it's between negative infinity and negative one For part B, we see a local minimum at sea of negative one, which is equal to negative three. Since that changes from decreasing to increasing report. See, we're finding the second derivative. Let me get for X minus two over nine x to the 5/3 and this is where the second derivative equal to thorough. So we get X is equal to two, and when X is equal to zero, it's undefined. So we take the intervals Negative infinity comma zero. We choose C double derivative of negative one and this is bigger than zero, which means it's calm. Keep up between the interval zero and two. We choose one just less than zero in between two and infinity, you choose three, which is bigger than zero. So the changes con cavity at zero and two. So there are inflection points zero comma zero into comma 7.56 When we plug it into the orginal equation Part D we just draw a graph and I love something like this

Numerade Educator

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