# 3.4 - Calculus Flashcards

I know understand what “rate of change” is

The rate of change is how quickly one variable changes as you vary another.

For example, in graphs we look at the gradient of a line - this is how “fast”

up or down a line moves as we go across the graph.

I can differentiate x5

5x4

I can differentiate 4x

4

I can differentiate x2 + 10

2x

I can find the gradient of a line by differentiating

For example, what is the gradient of the line given by this equation:

y = 4x^2^ + 2

at the point when x = 3?

Differentiating gives the gradient of the line:

dy/dx = 8x

= 8 × 3

= 24

What does it mean if the rate of change is 0?

The graph of the equation must be flat at this point - normally this is a turning point.

I can find the turning points of a line by differentiating

For example, what are the turning points of this equation:

y = 2x^2^ - 8x + 3

Differentiate to find the gradient equation:

dy/dx = 4x - 8

Turning points are when dy/dx = 0, so

0 = 4x - 8

x = 2

Substitute back into original equation to get y = 2x^2^ - 8x + 3 y = 2×2^2^ - 8×2 + 3 y = 2×4 - 16 + 3 y = 8 - 13 y = -5

Turning point is at (2, -5)

What is the rate of change of distance with respect to time?

Velocity - as time passes, something with a high velocity will move further

than something with a low velocity.

What is the rate of change of velocity with respect to time?

Acceleration - As time passes, something with high acceleration will pick up more speed than something with low acceleration.

Velocity changes faster when acceleration is high