### There are 16 results

Broad Topics >

Calculus > Differentiation

##### Age 16 to 18 Challenge Level:

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

##### Age 16 to 18 Challenge Level:

What functions can you make using the function machines RECIPROCAL and PRODUCT and the operator machines DIFF and INT?

##### Age 16 to 18 Challenge Level:

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

##### Age 16 to 18 Challenge Level:

Get started with calculus by exploring the connections between the
sign of a curve and the sign of its gradient.

##### Age 16 to 18 Challenge Level:

Build series for the sine and cosine functions by adding one term
at a time, alternately making the approximation too big then too
small but getting ever closer.

##### Age 16 to 18 Challenge Level:

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

##### Age 16 to 18 Challenge Level:

Can you hit the target functions using a set of input functions and a little calculus and algebra?

##### Age 16 to 18 Challenge Level:

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

##### Age 16 to 18 Challenge Level:

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

##### Age 16 to 18 Challenge Level:

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

##### Age 14 to 18

An article introducing the ideas of differentiation.

##### Age 16 to 18 Challenge Level:

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.

##### Age 16 to 18 Challenge Level:

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.

##### Age 16 to 18 Challenge Level:

Generalise the sum of a GP by using derivatives to make the
coefficients into powers of the natural numbers.

##### Age 16 to 18 Challenge Level:

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.

##### Age 16 to 18 Challenge Level:

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