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 $b$?