Consider the function below.C(x)=x15(x+6) (a) Find the interval of increase. (Enter your answer using interval notation.) Find the interval of decrease. (Enter your answer using interval notation.) b) Find the local minimum value(s). (Enter your answers as a comma-separated list. If an answer does not exist, enter DNE.) Find the local maximum value(s). (Enter your answers as a comma-separated list. If an answer does not exist, enter DNE.) (c) Find the inflection points. (x, y)=(?) (smaller x-value) (x, y)=(?) (large x-value) Find the intervals where the graph is concave upward. (Enter your answer using interval notation.) Find the interval where the graph is concave downward. (Enter your answer using interval notation.)

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Consider the function below.C(x)=x15(x+6)  (a) Find the interval of increase. (Enter your answer using interval notation.)  Find the interval of decrease. (Enter your answer using interval notation.)  b) Find the local minimum value(s). (Enter your answers as a comma-separated list. If an answer does not exist, enter DNE.)  Find the local maximum value(s). (Enter your answers as a comma-separated list. If an answer does not exist, enter DNE.)  (c) Find the inflection points.  (x, y)=(?) (smaller x-value)  (x, y)=(?) (large x-value)  Find the intervals where the graph is concave upward. (Enter your answer using interval notation.)  Find the interval where the graph is concave downward. (Enter your answer using interval notation.)

Latisha Oneil · Accepted Answer

Step 1Consider the function:f(x)=x15(x+6)a) (1) f′(x)=15π−45(x+6)+x15=x+65x45+x15=x+6+5x15+455x45=x+6+5x5x45=6(x+1)5x45For the critical points:f′(x)=0⇒6(x+1)5x45=0⇒x+1=0 and x≠0⇒x=−1 and x≠0The critical points are x=−1 and x=0Thus, the interval (−∞,−1), (−1,0), (0, ∞)In the interval (−∞,−1): Take x=−2f′(x)=6(−2+1)5(−2)45=−0.68&amp;lt;0⇒f(x) is decreasing in the interval (−∞,−1)In the interval (−1,0): Take x=−0.5f′(x)=6(−0.5+1)5(−0.5)45=1.04&amp;gt;0⇒f(x) is increasing in the interval (−1,0)In the interval (0,∞): Take x=1f′(x)=6(1+1)5(1)45=2.4&amp;gt;0

Consider the function below.C(x)=x^{\frac{1}{5}}(x+6) (a) Find the

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