Answer
$(y-2)=-4(x+1)$
Work Step by Step
Function: $f(x)=2x^2$ Line: $4x+y+3=0$
1. Find the slope $m$ of the given line by putting it into point-slope form:
$y=-4x-3$, $m=-4$
2. Take the derivative of the function:
$f'(x)=4x$
3. Set $f'(x)$ equal to $m$ and solve for the $x$-coordinate:
$4x=-4$
$x=-1$
4. Plug in $x$ from part 3 into $f(x)$ to get the $y$-coordinate:
$y=f(-1)=2(-1)^2=2$
Point: $(-1,2)$
5. Plug the slope $m$ and the point into the point-slope formula $(y-y_{1})=m(x-x_{1)}$:
$(y-2)=-4(x+1)$*
*In most cases point-slope form is sufficient. If not, simply convert into whatever form your professor deems acceptable.
