Tangent Line/Normal Line

Find the equation of the tangent line at the given point.
 $y=-\left(x+2\right)^{\frac{2}{3}\ }at\ \left(-1,-1\right)$  

•  $y=\frac{1}{2}x+2$  

•  $y=-\frac{2}{3}x-\frac{5}{3}$  

•  $y=-\frac{\sqrt{35}}{9}x-\frac{5\sqrt{35}}{9}$  

•  $y=\frac{1}{5}x+2$  

Find tangent line to the function at the given point:
 $y=-2x^2+4x-4\ at\ \left(0,\ -4\right)$  

•  $y=-2$  

•  $y=8x-2$  

•  $y=16x+14$  

•  $y=4x-4$  

Find the equation of the tangent line to the function at the given point:
 $y=\frac{5}{x^2+5}\ at\ \left(2,\frac{5}{9}\right)$  

•  $y=-\frac{5}{18}x+\frac{10}{9}$  

•  $y=1$  

•  $y=-\frac{20}{81}x+\frac{85}{81}$  

•  $y=\frac{15}{98}x+\frac{40}{49}$  

Find the equation of the tangent line to the function at the given point:
 $y=x^3-3x^2\ at\ \left(1,-2\right)$  

•  $y=24x-80$  

•  $y=-3x+1$  

•  $y=9x-27$  

•  $y=24x+28$  

Find the equation of the tangent line to the function at the given point:
 $y=x^3-3x^2+3\ at\ \left(0,\ 3\right)$  

•  $y=-1$  

•  $y=9x+8$  

•  $y=3$  

•  $y=24x+31$  

Find the equation of the normal line to the function at the given point:
 $y=-\frac{16x}{x^2+16}\ at\ \left(3,\ -\frac{48}{25}\right)$  

•  $y=\frac{625}{112}x-\frac{52251}{2800}$  

•  $y=\frac{25}{12}x-\frac{173}{30}$  

•  $y=\frac{625}{112}x+\frac{52251}{2800}$  

•  $Normal\ line\ is\ vertical\ line\ at\ x=-4$  

Find the equation of the normal line to the function at the given point:
 $y=-2x^2+12x-12\ at\ \left(3,\ 6\right)$  

•  $Normal\ line\ is\ vertical\ line\ at\ x=3$  

•  $y=-\frac{1}{16}x-\frac{417}{16}$  

•  $y=-\frac{1}{28}x-\frac{645}{7}$  

•  $y=-\frac{1}{8}x-\frac{15}{8}$  

Find the equation of the normal line to the function at the given point:
 $y=\left(2x+4\right)^{\frac{1}{3}}\ at\ \ \left(2,\ 2\right)$  

•  $y=2x+3$  

•  $y=-x+2$  

•  $y=-\frac{3\sqrt{5}}{2}x+\frac{2\sqrt{2}-9\sqrt{2}}{2}$  

•  $y=-6x+14$  

Find the equation of the normal line to the function at the given point:
 $y=\frac{2}{x^2-1}\ at\ \left(2,\ \frac{2}{3}\right)$  

•  $y=-\frac{9}{8}x-\frac{19}{12}$  

•  $y=-\frac{16}{3}x-\frac{63}{4}$  

•  $y=\frac{225}{16}x-\frac{3367}{60}$  

•  $y=\frac{9}{8}x-\frac{19}{12}$  

Find the equation of the normal line to the function at the given point:
 $y=-x^3+6x^2-9x-1\ at\ \left(3,\ -1\right)$  

•  $Normal\ line\ is\ vertical\ line\ at\ x=3$  

•  $y=-\frac{1}{3}x-\frac{7}{3}$  

•  $y=\frac{1}{72}x+\frac{2569}{24}$  

•  $y=\frac{1}{45}x+\frac{2207}{45}$