Question

pic

Answer 1

:)

Answer 2

Yay for trig equations.... lol
f(x) = 2sec(x) + tan(x)
f'(x) = 2sec(x)tan(x) + sec^2(x)

Set this equal to zero to get the critical numbers
2sec(x)tan(x) + sec^2(x) = 0

You can easily factor out sec(x) to get
sec(x)(2tan(x) + sec(x)) = 0 which gives us 2 equations

sec(x) = 0 which isn't possible since sec(x) is never equal to zero

2tan(x) + sec(x) = 0
by converting to sines and cosines we get

(2sin(x))/cos(x) + 1/cos(x) = 0
(2sin(x) + 1)/cos(x) since only the numerator matters for finding zeroes we now have

2sin(x) + 1 = 0
2sin(x) = -1
sin(x) = -1/2

Solve for x to get that our critical numbers are 7pi/6 and 11pi/6.

Answer 3

wow thank you :)

Answer 4

that was quick

Answer 5

You had it posted in the last question so i had already written that up :D

Answer 6

ok last 2

Answer 7

@jziggy

Answer 8

well, since f'(4) doesn't equal zero that would mean it isn't a critical number and therefore it can't be a minimum,maximum or point of inflection

Answer 9

At least I think.... haven't seen a problem in this format for a while haha

Answer 10

ok, so that narrows it down to, none right?

Answer 11

No, wait...

Answer 12

ok

Answer 13

Ok, I made a mistake in that

Answer 14

oh :P

Answer 15

if the second derivative = 0 and is less than 0 on one side and greater than zero on the other side it's an inflection point :)

Answer 16

ok sweet!

Answer 17

last one :P

Answer 18

@hilbertboy96 Thank you for the help...just mention me in a question sometime on physics for english and i will be able to help for sure

Answer 19

Again with the problems I've haven't done in a long time and this one looks complicated xD
So, we want to maximize 2xy + 3xy + 3xy + 2xy which is equal to 10xy

Answer 20

yes :)

Answer 21

Given the constraint, 8y +13x = 1040

Answer 22

solving for y gives us
8y = 1040 - 13x
y = (1040 - 13x)/8

Answer 23

hmmm it looks like 5x by 2x

Answer 24

that would give us 10 x

Answer 25

I don't trust pictures to be to scale :p