Question

Find a cubic function, in the form f(x)=ax^3+bx^2+cx+d, that has a local maximum value of 4 at -3 and a local minimum value of 0 at 2. f (x) = ax3 + bx2 + cx + d

Math to follow

Answer 1

\[f \prime(x)=3ax^2+2bx+c\]
\[f(-3)=4 => -27a+9b-3c+d\]
\[f(2)=0 => a+b+c+d\]
\[f \prime(-3)=0 =>27a-6b+c\]
\[f \prime(2)=0 => 12a+4b+c\]

Answer 2

\[\left(\begin{matrix}-27a+9b-3c+d=4 \\ -a+b+c+d=0\end{matrix}\right)=-28a+8b-4c=4\]
\[\left(\begin{matrix}27a-6b+c=0 \\-12a+4b+c=0\end{matrix}\right)=12a-10b=0\]

\[\left(\begin{matrix}-28a+8b-4c=4 \\ +4(12a+4b+c)=0\end{matrix}\right)=\left(\begin{matrix}-28a+8b-4c=4 \\ +48a+16b+4c=0\end{matrix}\right)\]
=20a+24b=4


I need to isolate a and b in order to get d, then c. Help...

Answer 3

Why don't you write a in terms of b?\[=20a+24b=4\ \ \rightarrow 5a +6b=1\rightarrow a= \frac{1-6b}{5}\]

Answer 4

You have a system of 2 equations: 12a−10b=0 and 20a +24b=4

Answer 5

I'm still unclear as to how to solve this

Answer 6

Which of the following best describes a line?
A. The set of all points in a plane that are equidistant from three points
B. The set of all points in a plane at a given distance from a given point
C. The set of all points in a plane that are equidistant from two points
D. The set of all points in a plane that are equidistant from a given point and a given line

Answer 7

That is not helpfully to me at all

Answer 8

I'm attempting to solve it in the manner which I've been shown. I'm not getting this