Question

15 POINTS!!: Find the equation of the tangent line to the parabola y=x^2 at the point (2, 4). Hint: A line y-4=m(x-2) is the tangent to the parabola if and only if the line is non-vertical and the nonlinear system

y=x^2
y=m(x-2)+4
has exactly one solution.

Answer 1

yeap, thus


`\bf y=x^2\implies \left. \cfrac{dy}{dx}=2x\right|_(x=2)\implies 4\qquad \\\\\\ y-{{ 4}}={{ 4}}(x-{{ 2}})\implies y-4=4x-8\implies y=4x-4\\ \left.\qquad \right. \uparrow\\ \textit{point-slope form}`