# 3.4 - Calculus Flashcards

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1
Q

I know understand what “rate of change” is

A

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.

2
Q

I can differentiate x5

A

5x4

3
Q

I can differentiate 4x

A

4

4
Q

I can differentiate x2 + 10

A

2x

5
Q

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?

A

Differentiating gives the gradient of the line:
dy/dx = 8x
= 8 × 3
= 24

6
Q

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

A

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

7
Q

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

A

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)

8
Q

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

A

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

9
Q

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

A

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