Wallis's method of tangents

[toopercent]

hi,
I am stuck on this question. Any hints will be appreciated.

consider the curve defined by the equation y=a(x^2)+bx+c. Take a point(h,k) on the curve. use Wallis's method of tangents to show that the slope of the line tangent to this curve at the point(h,k) will be m= 2ah+b. have to prove this for tow cases: a>0 and a<0.

Thank you

 

[morson]

Differentiating, dy/dx = 2ax + b

At the point (h, k), dy/dx = 2ah + b, hence the tangent's slope at this point is 2ah + b, since
the slope at any point on a curve (dy/dx) is equal to the slope of the tangent to that point.

If a > 0, its vertex is the lowest point of the curve (a minimum).

If a < 0, its vertex is the highest point of the curve (a maximum).