Differentiation 1

Question 1

Derive by first principles formula

Answer 1

f’(x) = lim h -> 0 (f(x+h) - f(x))/h

Question 2

How do you find a local minimum?

Answer 2

Find the point where f’(x) = 0, to the left f’(x) is negative and to the right f’(x) is positive

Question 3

How do you find a local maximum?

Answer 3

Find the point where f’(x) = 0, to the left f’(x) is positive and to the right f’(x) is negative

Question 4

How do you find a point of inflection?

Answer 4

Find the point where f’(x) = 0, to the left and right f’(x) is positive/negative

Question 5

If f(x) has a stationary point at x = a, what does f’‘(a) > 0 mean?

Answer 5

The point is a local minimum

Question 6

If f(x) has a stationary point at x = a, what does f’‘(a) < 0 mean?

Answer 6

The point is a local maximum