Chapter 4 - Differentiation and Integration

Question 1

What is the formula for differentiation?

Answer 1

If f(x) = axⁿ, then f’(x) = naxⁿ⁻¹

Question 2

What is the Leibniz Notation?

Answer 2

Leibniz Notation is dy/dx whereas Newtonian notation is f’(x).

Question 3

How do you calculate whether a point in the function is a maximum or minimum?

Answer 3

At a maximum turning point, d²y/dx² < 0 (less than)

At a minimum turning point, d²y/dx² > 0 (greater than)

Question 4

What is the formula for integration?

Answer 4

∫xⁿdx = xⁿ⁺¹/n+1 + c, n≠-1

Question 5

State the formula for differentiation by first principles.

Answer 5