Geometrical Applications of Differentiation

Question 1

A stationary point (S.P) can be identified if…

Answer 1

dy/dx = 0

Question 2

A maximum turning point (T.P) can be identified if…

Answer 2

dy/dx = 0

dy/dx= positive → 0 → negative

d2y/dx2 < 0

Question 3

A minimum turning point (T.P) can be identified if…

Answer 3

dy/dx = 0

dy/dx= negative → 0 → positive

d2y/dx2 > 0

Question 4

A horizontal point of inflection can be identified if…

Answer 4

dy/dx = 0

dy/dx = (m) → 0 → (m), gradient doesn’t change
dy^2/d^2x, DOES change

Question 5

A (vertical) point of inflection (P.O.I) can be identified if…

Answer 5

d2y/dx2 = 0

dy^2/d^2x, DOES change

Question 6

Graphing Technique:

1. Intercepts for y and x can be found by…

Answer 6

to find y intercepts:
make x = 0

to find x intercepts:
make y or f(0) = 0

Question 7

Graphing Technique:

2. Whether a function is even, odd or neither can be found by…

Answer 7

even:
f(x) = f(-x), symmetrical about y-axis

odd:
-f(x) = f(-x), rotational symmetry about 0,0

neither:
follows none of the above

Question 8

Graphing Technique:

3. horizontal (y-asymptote) and vertical (x-asymptote) asymptotes can be found by…

Answer 8

horizontal asymptotes:
see what happens when x → ∞ (outside the graph)

vertical asymptotes:
if fraction form, take denominator out and make it = 0

Question 9

Graphing Technique:

4. what do you consider when graphing?

Answer 9

domain and range

more specifically, the limits of the domain and range if stated in the question

Question 10

Graphing Technique:

5. what is your last resort in drawing graphs?

Answer 10

calculus to find S.P, T.P, P.O.I, etc…

Question 11

Graphing Technique:

6. what should you indicate on the graph

Answer 11

S.P, T.P, P.O.I, intercepts, domain/range (if there are limits)

i.e. its nature

Question 12

Min or max value of area that can be found can be done by…

Answer 12

using calculus to find min or max turning point (dy/dx = 0 and is changing)

Question 13

Will all shapes with the same perimeter have the same area

Answer 13

no

do the math pal… alright fine
a square with 10 by 10 by 10 by 10, P = 40u, A = 100u2
a rectangle with 6 by 6 by 14 by 14, P = 40u, A = 84u2

Question 14

The nature of graph means?

Answer 14

whether it’s a minimum T.P or max T.P, etc.

and WHERE is this occurance?

Question 15

Concavity refers to?

Answer 15

how the graph points up from a S.P

concave up = smiley
concave down = frowny