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 to the curve $y = \frac{e^x}{x^2}$ at $x = 1$.

Find the equations of the tangent and normal to the curve $y = e^x \ln(x^2+1)$ at $x = 0$.

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

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

Find the equations of the tangent and normal to the curve $y = \dfrac{e^{2x}}{\ln x}$ at $x = e$.

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

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

[7 marks]

Find the equations of the tangent and normal to the curve $y = (2x+1)e^{x^2}$ at $x = 0$.

Find the equations of the tangent and normal to the curve $y = x^2e^{3x}$ at $x = 0$. [5 marks]

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

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