Question

P (x, y) and Q (x+h, y+k) lie on the curve y=x²-3x. Find the gradient of PQ. I'm getting k/h, but the answer is 2x + h - 3. Help please?

Answer 1

\[y+k=(x+h)^2-3(x+h)=x^2+2xh+h^2-3x-3h=\]
\[=\underbrace{x^2-3x}_{=y}+2xh-3h+h^2\quad\Rightarrow\quad k=2xh-3h+h^2\]\[grad\,(PQ)=\frac{k}{h}=\frac{2xh-3h+h^2}{h}=2x-3+h\]