Question

Find the coordinates of the point on the curve y=7-3x-2x² where the gradient is 5​

Answer 1

the slope goes by several names

• average rate of change

• rate of change

• deltaY over deltaX

• Δy over Δx

• rise over run

• gradient

• constant of proportionality

however, is the same cat wearing different costumes.

`y=7-3x-2x^2\implies \cfrac{dy}{dx}=-3-4x\implies \stackrel{\textit{setting the derivative to 5}}{5=-3-4x} \\\\\\ 8=-4x\implies \cfrac{8}{-4}=x\implies \boxed{-2=x} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{when x = -2, what's`