Geometrical applications of differentiation (Chapter 6)

Question 1

For the sign of the first derivative:
f’(x)>0

Answer 1

function is increasing

Question 2

For the sign of the first derivative:
f’(x)<0

Answer 2

function is decreasing

Question 3

For the sign of the first derivative:
f’(x)=0

Answer 3

there is a stationary point

Question 4

A curve is monatonically (always) increasing or decreasing if f’(x) is > 0 for ___ x

Answer 4

ALL

Question 5

At a minimum point,
– curve is ___ on LHS
– curve is ___ on RHS

Answer 5

decreasing, increasing

Question 6

At a maximum point,
– curve is ___ on LHS
– curve is ___ on RHS

Answer 6

increasing, decreasing

Question 7

Points of inflection are defined as where curves are increasing OR decreasing on ____ sides of a gradient of stationary point

Answer 7

BOTH

Question 8

determining nature of stationary points = finding out what type of _____ they are

Answer 8

stationary point (min/max)

Question 9

the sign of the 2nd derivative indicates _____

Answer 9

concavity

Question 10

For the second derivative:
f”(x) >0

Answer 10

concave up

Question 11

For the second derivative:
f”(x) <0

Answer 11

concave down

Question 12

For the second derivative:
f”(x) =0

Answer 12

stationary point–> POINT OF INFLECTION

Question 13

absolute highest/lowest y-value is a ____

Answer 13

GLOBAL maxima or minima

Question 14

highest/lowest y-value for a certain area is a ______

Answer 14

LOCAL minima or maxima