Answer:
A non-calculus solution follows afterward.
For a calculus solution, the gradient is the first derivative with the point put in.
y = -x²+3x
dy/dx or y’ = -2x +3 is the gradient at any point.
but the tangent is at x = 2 so put it in
y’ = -(2*2)+3 = -1 is the gradient of the tangent at point (2,2)
Non-calculus solution:
y = -x²+3x 1️⃣but slope of tangent m = (y-2)/(x-2)2️⃣
put 1️⃣ into 2️⃣ and rearrange ⟹ mx-2m+x²-3x+2 = 0
or x²+(m-3)x+2–2m =0
but for a tangent the discriminant b²-ac = 0
(m-3)²-4*1*(2–2m) = 0
m²+2m+1 = 0
(m+1)(m+1) = 0
m = -1 is the is the gradient of the tangent at point (2,2)
Step-by-step explanation:
