so for part b)
y'(x) = 2x+b
when x = 3, the gradient is 5
So
5=2(3)+b
5=6 +b
-1=b
Sub x=3 and b = -1 into y=x^2+bx+c
y=(3)^2+(-1)(3)+c
y=6+c
Then the second part
y'(x) = 2x+b
when x = 2, the gradient is 0...
a) Differentiate y=x^2+bx+c, and hence find b and c, given that the parabola is tangent to the x-axis at the point (5,0)
b) Differentiate y=x^2+bx+c, and hence find b and c, when x =3 the gradient is 5, and x=2 is a zero.