First Principles And Derivatives

Question 1

What is the gradient of a curve?

Answer 1

The gradient of a curve at a given point is defined as the gradient of the tangent to the curve at that point?

Question 2

What does the derivative allow you to do?

Answer 2

Allows you to find the exact gradient of a curve at a given point

The closer the two points the more accurate the gradient is
The further away the points are the gradient is less accurate

Question 3

What is the equation of the first derivative for y=?

Answer 3

dy/dx

Question 4

What is the equation of the derivative for a function?

Answer 4

Derivative = f’(x)

Question 5

What does tending to zero mean?

Answer 5

When the difference between the two points is almost negligible that we disregard the h value and make it = 0

Question 6

What is differentiating from first principles (f(x) or y=)

Answer 6

f’(x) = lim h->0 (( f(x+h)-f(x))/ h )

Question 7

What can the gradient function be used to do?

Answer 7

The gradient of the curve for any value of x

Question 8

What is differentiating?

Answer 8

When you can use the definition of the derivative to find an expression for the derivative of x^n where n is any number.

Question 9

What happens if f(x) = x^n

And a is a constant

Answer 9

Then f(x) = x^n

nx^n-1

Question 10

What happens if y=x^n?

And a is a constant?

Answer 10

Then dy/dx =

nx^n-1

Question 11

What happens if f(x) = ax^n

Answer 11

Then f’(x) =

anx^n-1

Question 12

What happens if y=ax^n?

Answer 12

Then dy/dx=

anx^n-1