Question 1205498
<br>
{{{y=-x^2-3x+4}}}
{{{dy/dx=-2x-3}}}<br>
At x=2...
{{{y=-4-6+4=-6}}}
{{{dy/dx=-4-3=-7}}}<br>
The equation of the tangent line to the curve at (2,-6) is<br>
{{{y=mx+b}}}
{{{y=-7x+b}}}
{{{-6=-7(2)+b}}}
{{{-6=-14+b}}}
{{{b=8}}}<br>
{{{y=-7x+8}}}<br>
ANSWER: y=-7x+8<br>
A graph, showing a tangent at (2,-6)<br>
{{{graph(400,400,-1,3,-15,1,-x^2-3x+4,-7x+8)}}}<br>