IB Mathematics Applications & Interpretation Question Type 3: Finding the Tangent and Normal to More Complex Functions Using the GDC at Different Points Exercises

Find the equations of the tangent and normal lines to the curve $y=\ln (\sin x)+x^2$ at $x=\frac{\pi }{4}$.

Find the equations of the tangent and normal lines to the curve $y=x^x+e^x$ at $x=1$.

Find the equations of the tangent and normal lines to the curve $y=x^2{e}^{-x}$ at $x=0.5$.

Find the equations of the tangent and normal lines to the implicitly defined curve $x^2+xy+y^2=7$ at the point $(1,2)$.

Find the equations of the tangent and normal lines to the curve $y=e^{2x}\ln x+5x^3$ at $x=1$.

Find the equations of the tangent and normal lines to the curve $y=\frac{x+1}{x-1}+e^x$ at $x=2$.

Find the equations of the tangent and normal lines to the curve $y=x^3\ln x$ at $x=2$.

Find the equations of the tangent and normal lines to the parametric curve $x=t^2-1$ and $y=\ln t$ at $t=1$.

Find the equations of the tangent and normal lines to the curve $y=\sqrt{x}{e}^{3x}$ at $x=4$.

Find the equations of the tangent and normal lines to the curve $y=\ln (x^2+1)$ at $x=1$.

Find the equations of the tangent and the normal to the curve $y=e^{x^2}$ at the point where $x=1$.

Find the equations of the tangent and normal lines to the curve $y=x^x$ at $x=2$.