Page:Calculus Made Easy.pdf/112

 the point where the tangent touches the curve has $$x=2$$ for abscissa.

(8) At what angle do the two curves

$y=3.5x^2+2$ and $y=x^2-5x+9.5$

cut one another?

(9) Tangents to the curve $$y=\pm\sqrt{25-x^2}$$ are drawn at points for which $$x=3$$ and $$x=4$$. Find the coordinates of the point of intersection of the tangents and their mutual inclination.

(10) A straight line $$y=2x-b$$ touches a curve $$y=3x^2+2$$ at one point. What are the coordinates of the point of contact, and what is the value of $$b$$?