S.O.S. Mathematics CyberBoard

Find the acute angle between the tangent lines to the point of the intersection,different to the origin, between the the parabolas with the eq. =x and

Hello, PiDeltaPhi!

y = x^(1/2) and y = x^2 intersect at (0,0) and (1,1).

The derivatives are, respectively: y' = 1/2sqrt(x) and y' = 2x
The slope of the tangents at (1,1) are: m1 = 1/2 and m2 = 2

The tangent of angle A is given by: (m2 - m1)/(1 + m1*m2)

Hence, tan(A) = (3/2)/(2) = 3/4
and A = 36.87 degrees

[Interesting -- The angle comes from the ubiquitous 3-4-5 triangle!]