Week 3

Question 1

When a function is STRICTLY increasing or decreasing?

Answer 1

f’(x) > 0 in the interval
f’(x) < 0 in the interval

Question 2

Local maximum vs strict local maximum?

Answer 2

• local max means that it is maximum or equal to in that area

-strict local maximum means that it is only maximum in given area

Question 3

Stationary inflection point and normal inflection point?

Answer 3

-point where it is not a local min or max f’(x) =0

inflection point = f’‘(x) = 0 and changes sign around x

Question 4

Second derivative test?

Answer 4

f’‘(x) >0 strict local min
f’‘(x)<0 strict local max

Question 5

First derivative test for strict maxima?

Answer 5

-Miss Crabb table

Question 6

Convex Concave?

Answer 6

for given domain
-F’‘(x)>0 = convex
F’‘(x)<0 = concave

Question 7

Equation for a stretched circle about x-axis?

Answer 7

x^2/a^2 + y^2/ b^2 = 1

where b is y intercept and a is x intercept

Question 8

Two symmetrical concave curves equation?

Answer 8

x^2/a^2 - y^2/ b^2 = 1

asymptote is y = +- bx/a

Question 9

Global maximum or strict global maximum?

Answer 9

-global maximum is f(x) is greater or equal maximum
strict global maximum is f(x) is the greatest