2.2.15 The graph and equation of the function f are given. a. Use the graph to f

Question

2.2.15 The graph and equation of the function f are given. a. Use the graph to find any values at which f has a relative maximum, and use the equation to calculate the relative maximum for each value b. Use the graph to find any values at which fhas a relative minimum, and use the equation to calculate the relative minimum for each value fx)-23 +32 -12x 19 I-5,5.1] byf 35,35,5] a. Select the correct choice below and, if necessary, fill in the answer boxes to complete your choice. A The function f has a relatre m ima maximum 0 B.. The function f has no relative maxima. at and the relative maxima(maximum) are is (Use a comma to separate answers as needed.)

Explanation / Answer

given f(x)=2x3+3x2-12x+9

a)from the graph relative maximum appears to be at x=-2

relative maximum =f(-2)

relative maximum=2(-2)3+3(-2)2-12(-2)+9

relative maximum=-16+12+24+9

relative maximum=29

the function has a relative maxima at -2 and the relative maxima is 29

b)from the graph relative minimum appears to be at x=1

relative minimum =f(1)

relative minimum=2(1)3+3(1)2-12(1)+9

relative minimum=2+3-12+9

relative minimum=2

the function has a relative minima at 1 and the relative minima is 2

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