Skip to main content
### Number and algebra

### Geometry and measure

### Probability and statistics

### Working mathematically

### For younger learners

### Advanced mathematics

# It's Only a Minus Sign

Remember that the differential of x means the 'rate of change' of $x$. The equation tells us exactly what that rate of change must be at each point.

What does a positive rate of change tell us about the changes in $x$? What does a negative rate of change tell us about the changes in $x$?

## You may also like

### Circles Ad Infinitum

### Climbing Powers

Or search by topic

Age 16 to 18

Challenge Level

- Problem
- Getting Started
- Student Solutions
- Teachers' Resources

Remember that the differential of x means the 'rate of change' of $x$. The equation tells us exactly what that rate of change must be at each point.

What does a positive rate of change tell us about the changes in $x$? What does a negative rate of change tell us about the changes in $x$?

A circle is inscribed in an equilateral triangle. Smaller circles touch it and the sides of the triangle, the process continuing indefinitely. What is the sum of the areas of all the circles?

$2\wedge 3\wedge 4$ could be $(2^3)^4$ or $2^{(3^4)}$. Does it make any difference? For both definitions, which is bigger: $r\wedge r\wedge r\wedge r\dots$ where the powers of $r$ go on for ever, or $(r^r)^r$, where $r$ is $\sqrt{2}$?