IB Mathematics Applications & Interpretation Topic SL…

The cross-section of a garden arch is modeled by the polynomial $y=(x-4)(x^2-5x+8)$ .

Obtain an expression for $\frac{dy}{dx}$ .

Calculate the equation of the normal line to the curve at the point where .

Find an expression for $\frac{\mathrm{d}y}{\mathrm{d}x}$ .

An engineer models the cross-section of a reflector by $r(x)=\frac{3}{2}(x-6)^2+7$ , where and are measured in centimetres.

Determine the horizontal intercept of the tangent line $l$ drawn to the graph of $g(x)=2x^3-5x^2+4x+1$ at the coordinate point .

Consider the function $h$ defined by $h(x)=x^3-3x+5$ .

Find the equations of the tangent and the normal to this curve at the point where it crosses the $y$ -axis.

Calculate the derivative $r'(x)$ .

Find the slope of the tangent line at $x=8$ .

Find the equation of the normal line to the function at $x=8$ .

Determine the value of $x$ for which the slope of the tangent is $0$ .

State the domain and range of the function $r(x)$ .

Calculate the equation of the line normal to the graph of $y=h(x)$ at the point $(2,7)$ in the form $ax+by+d=0$ , where $a,b,d\in\mathbb{Z}$ .

IB Mathematics Applications & Interpretation SL 5.4—tangents and Normals Questionbank