Question

question about first derivative tests..

Answer 1

is there anything special about second derivative test?

Answer 2

also, i have this problem where im asked to find the increasing and decreasing intervals of a function, but i have this.. (from solution manual) problem E. http://vvcap.net/db/nHLQ8VZBD4XAvL3N4VTp.htp

Answer 3

Yes. The second derivative test determines concavity and can tell if you have a maximum (if it is concave down) or a minimum (if it is concave up). Once you know you have a relative extrema at a certain x-value, you could just take the second derivative of the function to determine max/min instead of looking at the behavior around the extrema.

Answer 4

im not sure what to do aftee cosx<1/2 intervals of my original f(x) is 0<x<3pi

Answer 5

If you have the function, take the derivative. When f'(x) is greater than zero, it is increasing. When f'(x) is less than zero, it is decreasing. Use ( ) instead of [ ] because it doesn't include when it it isn't changing.

Answer 6

the 2nd derivative test is used to determine the nature of the stationary points found at the 1st derivative,

it saves testing either side of the 1st derivative to look for changes in slope.

2nd derivative test is quicker and neater

Answer 7

not sure how they got those intervals.

Answer 8

thanks for the info guys!

Answer 9

if a is a stationary point in from the 1st derviative

f"(a) > 0 then a min occurs at a

f"(a) < 0 then a max occurs at a

f'(a) = 0 then a horizontal point of inflexion

Answer 10

how do i link cosx <1/2 ----> ?

Answer 11

the decreasing and increasing intervals comes from the 1st derivative... its really asking over what interval would a tangent have a positive slope... increasing, negative slope, decreasing, ... no slope, stationary point

Answer 12

hmmm okay.. i think i just need to let it soak in a bit.thanks!