Ch.12 Differentiation

Question 1

what is the gradient of a curve at a given point defined as?

Answer 1

the gradient of the tangent to the curve at that point

Question 2

what is the derivative?

Answer 2

the gradient function of the curve

Question 3

how is the derivative written?

Answer 3

f’(x) = dy/dx = lim h>0 f(x+h) - f(x) / h

Question 4

how would you differentitaite a term like x to the power of n?

Answer 4

multiply by power then subtract 1 from the power

Question 5

what is the normal to the curve at point?

Answer 5

a straight line perpendicular to the tangent at point A

Question 6

how would you know if a curve is increasing?

Answer 6

if the gradient is greater than or equal to 0 ( if its positive )

Question 7

how would you know if a curve is decreasing?

Answer 7

if the gradient is lesser than or equal to 0 ( if its negative )

Question 8

what is a stationary point?

Answer 8

any point on the curve where f’(x) = 0

Question 9

what is a local maximum stationary point?

Answer 9

shaped like a “n” and has a gradient change from positive to 0 to negative

• second order derivative will be less than or equal to 0

Question 10

what is a local minimum stationary point?

Answer 10

shaped like a “u” and has a gradient change from negative to 0 to positive

• second order derivative will be greater than or equal to 0

Question 11

what is a point of inflection?

Answer 11

stationary point that has a gradient change of positive to 0 to positive or negative to 0 to negative