Sign In | Starter Of The Day | Tablesmaster | Fun Maths | Maths Map | Topics | More

- 5.4 Tangents and Normals
- 5.7 Second Derivative
- 5.8 Turning Points

This page should remember your ticks from one visit to the next for a period of time. It does this by using Local Storage so the information is saved only on the computer you are working on right now.

Here are some related resources in alphabetical order. Some may only be appropriate for high-attaining learners while others will be useful for those in need of support. Click anywhere in the grey area to access the resource.

- Maxvoltray Find the maximum volume of a tray made from an A4 sheet of paper. A practical mathematical investigation.
- Differentiation Video A reminder of how to differentiate different types of functions and how to find the equations of tangents and normals.
- Differentiation Practise the technique of differentiating polynomials with this self marking exercise.

Here are some exam-style questions on this topic:

- "
*The table shows some values (rounded to one decimal place) for the function \(y=\frac{2}{x^2}-x, x\neq 0\).*\(x\) -3 -2 -1 -0.5 0.5 1 2 3 4 \(y\) 3.2 2.5 8.5 7.5 1.0 -2.8 *(a) Complete the table of values.*" ... more - "
*A function is given as \(f(x)=3x^2-6x+4+\frac3x,-2\le x \le 4, x\ne 0\).*" ... more - "
*Consider the graph of the function \(f(x)=7-3x^2-x^3\)*" ... more - "
*A child's play tent is made in the shape of half a cylinder. It is constructed from a fibreglass frame with material pulled tightly around it. The fibreglass frame consists of a rectangular base, two semi-circular ends and two further support rods, as shown in the following diagram.*" ... more - "
*A package is in the shape of a cuboid and has a length \(l\) cm, width \(w\) cm and height of 12 cm.*" ... more - "
*Consider the function \(f(x)=6 - ax+\frac 3{x^2},x\neq 0\)*" ... more - "
*Consider the function \(f\) defined by \(f(x)= \ln{(x^2 - 9)}\) for \(x > 3\).*" ... more - "
*The function \(f\) is defined for all \(x \in \mathbb{R}\). The line with equation \(y=5x+3\) is the tangent to the graph of \(f\) at \(x = 2\)*" ... more - "
*Consider the cubic function \(f(x)=\frac{1}{6}x^3-2x^2+6x-2\)*" ... more - "
*Consider the function \(f(x)=x^3-9x+2\).*" ... more - "
*Let \(f(x)=\frac{g(x)}{h(x)}\), where \(g(3)=36\), \(h(3)=12\), \(g'(3)=10\) and \(h'(3)=4\). Find the equation of the normal to the graph of \(f\) at \(x=3\).*" ... more - "
*The displacement, in millimetres, of a particle from an origin, O, at time t seconds, is given by \(s(t) = t^3 cos t + 5t sin t\) where \( 0 \le t \le 5 \) .*" ... more - "
*A circle with equation \(x^2+y^2=25 \) has centre \((0,0)\) and radius 5.*" ... more - "
*Consider the functions*" ... more - "
*The following diagram shows part of the graph of \(y=f (x)\)*" ... more - "
*Moresum Soup is sold in cans with a capacities of 400ml each. Each can is in the shape of a right circular cylinder with radius \(r\) cm and height \(h\) cm.*" ... more - "
*The following diagram shows the graph of \(f'\), the first derivative of a function \(f\).*" ... more - "
*Let \(f(x) = \frac{ln3x}{kx} \) where \( x \gt 0\) and \( k \in \mathbf Q^+ \).*" ... more - "
*Consider the function \(f(x)=\frac{20}{x^2}+kx\) where \(k\) is a constant and \(x\neq0\).*" ... more

Here are some Advanced Starters on this statement:

**Fence Optimisation**

Find the length of a rectangle enclosing the largest possible area. more**Road Connections**

Design roads to connect four houses that are on the corners of a square, side of length one mile, to minimise the total length of the roads. more

Click on a topic below for suggested lesson Starters, resources and activities from Transum.

This Scheme of Learning was produced by White Rose Maths and is used here with permission granted on 30th June 2021.