SOLUTION: graph each function. find any local maxima or minima to the nearest tenth. find intervals over which the function is increasing. p(x)=4x^3-3x^2+2,-6≤x≤6

Algebra ->  Trigonometry-basics -> SOLUTION: graph each function. find any local maxima or minima to the nearest tenth. find intervals over which the function is increasing. p(x)=4x^3-3x^2+2,-6≤x≤6      Log On


   



Question 348960: graph each function. find any local maxima or minima to the nearest tenth. find intervals over which the function is increasing.
p(x)=4x^3-3x^2+2,-6≤x≤6

Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
graph%28300%2C300%2C-7%2C7%2C-20%2C20%2C4x%5E3-3x%5E2%2B2%29
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The derivative of p(x) is,
dp%2Fdx=12x%5E2-6x
The derivative equals zero when,
12x%5E2-6x=0
6x%282x-1%29=0
Two solutions,
x=0 where p%28x%29=4%280%29%5E3-3%280%29%5E2%2B2=2
Local maxima
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2x-1=0
2x=1
x=1%2F2 where p%28x%29=4%281%2F2%29%5E3-3%281%2F2%29%5E2%2B2=4%2F8-3%2F4%2B2=7%2F4
Local minima
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From the graph you can pick out the intervals where the function is increasing and decreasing.