Question heo Help 4 on the in [-10,0 Find the derivative of f(x)3x+36x+108x+4 r)

Question

Question heo Help 4 on the in [-10,0 Find the derivative of f(x)3x+36x+108x+4 r)-+72x+ 108 Identify the absolute maximum ifit exists, as well as all values of x where it occurs. Select the correct choice below and, if necessary, il in the answer boxes to O A. The absolute maximum is?which occurs atxz Round the separate answers as needed.) e maximum to teo decimal laeces as neded Type an exad answer for the madimum ocurs Use a comma to O B. There is no absolute maximum Click to select and enter your answer(s) and then click Check Answer part Clear All 0

Explanation / Answer

f(x) =3x^3+36x²+108x+4

find derivative as

f'(x) = 9x² +72x +108

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Now to find critical point, solve f'(x) = 0

9x² +72x +108 =0

9(x²+8x+12) =0

9(x+6)(x+2)=0

x =-6, -2

Now evalaute function at critical point and endpoint as

f(-6) = 4

f(-2) = -92

f(-10) = -476

f(0) = 4

hence Absolute maximum is 4 which occurs at x= -6,0

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Also Absolute minimum is -476 which occurs at x= -10

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