f(0) = 2(3)(0) = 0 ⇒ (0, 0)
f(1) = 2(3)(1) = 6 ⇒ (1, 6)
<u>rate of change from x = 0 to x = 1</u>
=
=
= 6
******************************************
f(2) = 2(3)(2) = 12 ⇒ (2, 12)
f(3) = 2(3)(3) = 18 ⇒ (3, 18)
<u>rate of change from x = 2 to x = 3</u>
=
=
= 6
*****************************************
Since it is the same line, they will have the same slope (aka rate of change).
Answer:
The diagonal is increasing at the rate of 119/104cm/min of the given rectangle.
Step-by-step explanation:
Dimensions of the rectangle
Height = 5cm
Rate of base = 3/2 cm/min
Area = 60cm^2
We know the area of a rectangle of given by = base* Height
b*h = 60
b*5 = 60
b = 12cm
Applying Pythagoras theorem while drawing a diagonal to the rectangle
so our diagonal will be 13cm
Upon differentiating the area of the rectangle we get
b*h = A=60cm^2
using the chain rule of differentiation
h*db/dt + b*dh/dt = 0
b*dh/dt = -h*db/dt
12*dh/dt = -5*3/2
dh/dt = -5/8 cm//min
so the height of the rectangle is decreasing at the rate of -5/8cm/min
now we have all the measurements we need
b = 12 , db/dt = 3/2cm/min
h = 5 , dh/dt = -5/8 cm/min
Upon differentiating we get
2b*db/dt + 2h*dh/dt = 2D*dD/dt
b*db/dt + h*dh/dt = D*dD/dt
12*3/2 + 5*(-5/8) = 13*dD/dt
18 -25/8 = 13*dD/dt
= 13*dD/dt
dD/dt =
Therefore the diagonal is increasing at the rate of 119/104cm/min of the given rectangle.