## anonymous 4 years ago Calc Q: given a fxn f(x)=x^3+ax^2+bx+k, where a,b,and k are constants. The fxn has a local min at x=-1 and an inflection point at x=-2. a. find the values of a and b b. if the integral of f(x)dx=32 (from 0 to 1), what is the value of k? just need a general idea of process.

1. myininaya

find f' $f'(x)=3x^2+2ax+b$ Since x=-1 is a min then f'(-1)=0 so we have $f'(-1)=3+2a(-1)+b=0=> -2a+b=-3$ find f'' $f''(x)=6x+2a$ Since x=-2 we have an inflection point then f''(-2)=0 so we have $f''(-2)=6(-2)+2a=0 => 2a=12=>a=6$ if a=6 then -2(6)+b=-3 => -12+b=-3 => b=-3+12=9

2. myininaya

$\int\limits_{0}^{1}(x^3+6x^2+9x+k) dx=32$

3. anonymous

Thank you!!

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