- #1
greg_rack
Gold Member
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- Homework Statement
- Given the function ##y=ax^3+bx^2+2x-1##, find which values must ##a## and ##b## assume in order to have a relative maximum for ##x=-1##.
- Relevant Equations
- none
The derivative of a point of maximum must be zero, and since
$$y'=3ax^2+2bx+2 \rightarrow y'(-1)=3a-2b+2 \rightarrow 3a-2b+2=0$$
we get the first condition for ##a## and ##b##.
Now, since we want ##x=-1## to be a local maximum, the derivative of the function must be positive when tending to the left of ##x=-1##, and negative when tending to the right of ##x=-1##.
I believe this is the second point that would allow me to get ##a## and ##b##... but I don't know how to "write it down" as a formal condition.
$$y'=3ax^2+2bx+2 \rightarrow y'(-1)=3a-2b+2 \rightarrow 3a-2b+2=0$$
we get the first condition for ##a## and ##b##.
Now, since we want ##x=-1## to be a local maximum, the derivative of the function must be positive when tending to the left of ##x=-1##, and negative when tending to the right of ##x=-1##.
I believe this is the second point that would allow me to get ##a## and ##b##... but I don't know how to "write it down" as a formal condition.