Differentiation

Question 1

When the function is decreasing what happens to the tangent lines to the curve?

Answer 1

They have a negative slope.

Question 2

When the function is increasing what happens to the tangent lines to the curve?

Answer 2

They have a positive slope.

Question 3

If the derivative f’ is greater than zero for x in (a, b) what is happening to the original graph?

Answer 3

F is increasing on (a, b).

Question 4

If the derivative f’ is less than than zero for x in (a, b) what is happening to the original graph?

Answer 4

F is decreasing on (a, b).

Question 5

What is the first derivative test?

Answer 5

Used to locate relative extrema of f.

Question 6

If c is defined as a critical number then what happens if f’x changes from positive to negative at x =c?

Answer 6

The f has a relative maximum point at (c, f(c)).

Question 7

If c is defined as a critical number then what happens if f’x changes from negative to positive at x =c?

Answer 7

The f has a relative minimum point at (c, f(c)).

Question 8

If f’‘x is greater than zero for all x in (a, b) then what is happening to the original graph?

Answer 8

F is concave up on (a, b).

Question 9

If f’‘x is less than zero for all x in (a, b) then what is happening to the original graph?

Answer 9

F is concave down on (a, b).

Question 10

What are the points on the graph where the concavity changes and what are the conditions for this?

Answer 10

Inflexion points - if f’‘x = 0 and changes sign.