Question

Calculus rate of change/derivatives: Did I do this right?

Answer 1

no

Answer 2

lol

Answer 3

The length L of a rectangle is decreasing at the rate of 2cm/sec while the width W is increasing at the rate of 2cm/sec. when l=12 cm and w=5cm, find the rates of change of a) the area, b) the perimeter, c) the lenght

Answer 4

For the rate of change of the area I got 240 cm^2/sec

Answer 5

da/dt = da/dw*dw/dt + da/dl *dl/dt

Answer 6

*******ooops c) is the length of a diagonal of the rectangle ***********************

Answer 7

ROC of the perimeter= 48 cm/sec and the length a diagonal of the rectangle I got 34/13( I used the Pythagorean theorem, idk if it's correct) lol

Answer 8

Ohhh I forgot to use the product rule for a)

Answer 9

I have to use the product rule for a) right? rate of change of area

Answer 10

it is what it is

Answer 11

I get 34 cm^2/sec

Answer 12

That's the rate of change of the area.

Answer 13

da/dt = da/dw*dw/dt + da/dl *dl/dt
=L*2+w*2
=12*2+5*2 = 34

Answer 14

ye u right

Answer 15

Ok :) now for the rate of change of the perimeter, I got 48 cm/sec.

Answer 16

no

Answer 17

p=2l +2w

Answer 18

oh wait :O

Answer 19

The derivative of that is
dp/dt = 2*l*dl/dt + 2*w*dw/dt ?

Answer 20

its decreaing and increasing its not 34 for A

Answer 21

So it's negative.

Answer 22

da/dt = da/dw*dw/dt + da/dl *dl/dt =L*2+w*2 =12*-2+5*2 = -14

Answer 23

for P
P=2L+2W
dt/dt=dp/dl*dl/dt+dp/dw*dw/dt
=2*-2 + 2*2=0

Answer 24

intuitively shud make sense

Answer 25

if one side is going up by 2, and other is decreasing by 2

Answer 26

overall the perimeter is the same

Answer 27

so there is no change in perimeter

Answer 28

Ohh I see thanks ^_^

what about c), I used the Pythagorean theorem

Answer 29

YAH

Answer 30

D=sqrt(L^2+w^2)
dD/dt=dD/dl*dl/dt+dD/dw*dw/dt

Answer 31

something to note the right side is all partial derivativs

Answer 32

so for dw/dt where d is partial, the L is seen as a constant

Answer 33

dD/dw, L is constant

Answer 34

Wait... How is the derivative of D=sqrt(L^2+w^2) = dD/dt=dD/dl*dl/dt+dD/dw*dw/dt ?

Answer 35

What exactly does dD/dl mean?