Differentiation

problem
Favourite

Exponential Trend

Age

16 to 18

Challenge level

1 out of 3

Find all the turning points of y=x^{1/x} for x>0 and decide whether each is a maximum or minimum. Give a sketch of the graph.
problem
Favourite

Slide

Age

16 to 18

Challenge level

1 out of 3

This function involves absolute values. To find the slope on the slide use different equations to define the function in different parts of its domain.
problem
Favourite

Quick Route

Age

16 to 18

Challenge level

1 out of 3

What is the quickest route across a ploughed field when your speed around the edge is greater?
problem
Favourite

Loch Ness

Age

16 to 18

Challenge level

2 out of 3

Draw graphs of the sine and modulus functions and explain the humps.
problem

Bend

Age

16 to 18

Challenge level

1 out of 3

What is the longest stick that can be carried horizontally along a narrow corridor and around a right-angled bend?
problem

Bird-Brained

Age

16 to 18

Challenge level

1 out of 3

How many eggs should a bird lay to maximise the number of chicks that will hatch? An introduction to optimisation.
problem

Ramping It Up

Age

16 to 18

Challenge level

2 out of 3

Look at the calculus behind the simple act of a car going over a step.
problem

Impedance Can Be Complex!

Age

16 to 18

Challenge level

3 out of 3

Put your complex numbers and calculus to the test with this impedance calculation.
problem

Least of All

Age

16 to 18

Challenge level

1 out of 3

A point moves on a line segment. A function depends on the position of the point. Where do you expect the point to be for a minimum of this function to occur.
problem

Integration Matcher

Age

16 to 18

Challenge level

1 out of 3

Can you match the charts of these functions to the charts of their integrals?