Question

find the lines that are tangent and normal to the curve y=sqrtx at x=4

Answer 1

\[y=\sqrt{x}\quad,\quad M(4,2)\]\[y'=\frac{1}{2\sqrt{x}}\]\[y'(4,2)=\frac{1}{4}\]tangent:\[y-2=\frac{1}{4}(x-4)\]normal:\[y-2=-4(x-4)\]