Differentiation B1 Ch12

Question 1

What is the equation of differentiating from first principles?

Answer 1

f’(x)=f(x+h)-f(x)/h as h tends towards 0

Question 2

How do you differentiate axⁿ?

Answer 2

anx^(n-1)

Question 3

How can you work out if a graph is increasing at a certain point?

Answer 3

Differentiate and sub in values if gradient is positive then it is an increasing function

Question 4

How can you find the nature of a turning point

Answer 4

•Differentiate again to find f’’(x) •work out the gradient either side of the stationary point

Question 5

From the second derivative how will you know if it is a maximum point?

Answer 5

If f’’(x)<0 it is a point of maximum

Question 6

From the second derivative how will you know if it is a minimum point?

Answer 6

If f’’(x)>0 it is a point of minimum

Question 7

From the second derivative how will you know if it is a point of inflection?

Answer 7

If f’’(x)=0 it could be a point of inflection, max or min.

Question 8

If there is a maximum or minimum in the graph of y=f(x) what is there in the y=f’(x) graph?

Answer 8

Intersection of the x axis

Question 9

If there is a point of inflection in the graph of y=f(x) what is there in the y=f’(x) graph?

Answer 9

Touches the axis

Question 10

If there is a positive gradient in the graph of y=f(x) what is there in the y=f’(x) graph?

Answer 10

Above the x axis

Question 11

If there is a negative gradient in the graph of y=f(x) what is there in the y=f’(x) graph?

Answer 11

Below the x axis

Question 12

If there is a vertical asymptote in the graph of y=f(x) what is there in the y=f’(x) graph?

Answer 12

Vertical asymptote

Question 13

If there is a horizontal asymptote in the graph of y=f(x) what is there in the y=f’(x) graph?

Answer 13

Horizontal asymptote at the the x axis