g ( x ) = 150 + 8 x 3 + x 4 (a) Find the interval of increase. (Enter your answe

Question

g(x) = 150 + 8x3 + x4 (a)  Find the interval of increase.  (Enter your answer in interval notation.) Find the interval of decrease.  (Enter your answer in 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 interval where the graph is concave upward.  (Enter your answer in interval notation.) Find the interval where the graph is concave downward.  (Enter your answer in interval notation.) Find the inflection points. (x, y) =                   (smaller x value) (x, y) =                    (larger x value) PLEASE GIVE EXACT ANSWERS ONLY g(x) = 150 + 8x3 + x4 (a)  Find the interval of increase.  (Enter your answer in interval notation.) Find the interval of decrease.  (Enter your answer in 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 interval where the graph is concave upward.  (Enter your answer in interval notation.) Find the interval where the graph is concave downward.  (Enter your answer in interval notation.) Find the inflection points. (x, y) =                   (smaller x value) (x, y) =                    (larger x value) PLEASE GIVE EXACT ANSWERS ONLY

Explanation / Answer

g(x)=150 +8x^3+x^4

for g(x) to increase g'(x) >=0

g'(x)=24x^2+4x^3=4x^2(6x+1) x^2 is always positive so (6x+1)>=0 implies x>=-1/6 so g(x) is increasing in the interval

[-1/6 INF)

so g(x) is decresing in the interval (-INF -1/6]

b)g"(x) =48x+6x^2=6x(8x+1) it has only one critical point -1/6 and g"(x)<0 at x=-1/6 so it has local maxima at x=-1/6

and the value is 1/3

and g(x) does not have any local minima

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