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.

Question

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.

myininaya · Answer

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

myininaya · Answer

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

anonymous · Answer

Thank you!!