IB Mathematics Applications & Interpretation Question Type 2: Calculating the Normal to the Curve at the Point Where Tangent Is Known Exercises

Calculate the equation of the normal to the curve $y=x^2+2x+1$ at the point where the tangent is parallel to the line $y=4x+3$.

For the curve $y=3x^3-x$, find the equations of the normals at the points where the tangent is horizontal.

Find the equation of the normal to $y=4x^4-8x^2+5$ at $x=1$.

The normal to the curve $y=x^2+kx+3$ at $x=3$ has gradient $-\frac{1}{4}$. Find the value of $k$ and the equation of this normal.

Find the equation of the normal to the curve $y=x^5-5x+4$ at $x=2$.

Find the equation of the normal to the curve $y=x^4-2x+1$ at $x=1$.

For the curve $y=\frac{1}{x}$, find the equation(s) of the normal(s) at the point(s) where the tangent is parallel to the line $y=-x+4$.

The normal to $y=x^3-a{x}^2+bx-1$ at $x=1$ is $y=x+2$. Find the values of $a$ and $b$.

The tangent to the curve $y=2x^3+x^2-4x+1$ is $y=4x-4$. Find the equation of the normal at the point of contact.

Find the equation of the normal to the curve $y=x^2-4x+7$ at $x=2$.

Find the equations of the normals to the curve $y=x^3-3x+2$ at the points where the tangents are parallel to the line $y=9x-7$.

Find the equation of the normal to the curve $y=3x^3-x^2+2$ at the point where $x=-1$.