Question

Calculus EXPERTS help, pretty please

The rate of fuel consumption is increasing the fastest at time t = 22.5. What is the value of R''(22.5)? Explain your reasoning.

Answer 1

okay I realize 22.5 is in between 15 and 30 , but i have no idea how to go about finding the double prime? Please help me, Thank you so much!

Answer 2

So when you graph the curve, what would you have around 22.5?

Answer 3

looks like 45

Answer 4

so that's R(22.5)

Answer 5

not quite, I mean does it look like a hill or a valley

Answer 6

think about what it looks like not the actual pts

Answer 7

made this in excel. I can see the derivative would be increasing at this point

Answer 8

ooh goody, You're thinking on the right track, but the derivative would just be positive

Answer 9

now can you tell me what the derivative at the highest spot on that graph you showed me is?

Answer 10

when t=50 the derivative is 0

Answer 11

good and why?

Answer 12

because there is no slope,
how about at 22.5 ?

Answer 13

not the reason, what happens at t=50?

Answer 14

It is a ____________.

Answer 15

Well, the rate at which the fuel is consumed stops, begins to decrease

Answer 16

maximum

Answer 17

right,

Answer 18

yes!

Answer 19

oh, so at R"(22.5) it would also be 0? :)

Answer 20

yes can you tell me why?

Answer 21

because this is the maximum of the derivative of R(t). Fastest rate of consumption

Answer 22

yep! And the derivative (in this case)tells us that we have either a max or a min then its derivative =0

Answer 23

Thanks, you helped me think this one through! Medal :)

Answer 24

np good luck with calc!

Answer 25

Thanks!