Question

write a formula for the linearization L(x) of F(x) using this information:
F(x) = -x2 /2
F '(-2) = 2

Answer 1

i assume you want the linearization at x = -2

Answer 2

and that your function is
\[F(x)=-\frac{x^2}{2}\]

Answer 3

in which case you need a point and a slope, and you use the point-slope formula:
the point is
\[(-2,F(-2))\] in other words
\[(-2,-2)\]
and
\[m=F'(-2)=2\] so the linearization is
\[y-(-2)=2(x-(-2))\]
\[y+2=2x+4\]
\[y=2x+2\] or even
\[L(x)=2x+2\]

Answer 4

Thank you!

Answer 5

yw