Q2) x-axis tangent to the curve => curve touches the line y=0
only 1 time
so 3x^2-8x+5-k = 0 at only 1 point => 1 root
discriminant = 0
64 - 4(3)(5-k) = 0
4+12k = 0
k = -1/3 => help me check... all done without using paper... so
not confirmed
Find value of x: 2 methods
1st method:
3x^2-8x+16/3 = 0
9x^2-24x+16 = 0
(3x - 4)^2 = 0
x=4/3
and y = 0 (on x-axis mah)
coordinates: (4/3, 0)
2nd method:
obviously, for an x^2 curve, ie curve with smiling face, the
minimum point will be the point at tangent with the x-axis.
so dy/dx = 6x-8
x = 4/3 (same answer)