Answer:
(a) The power reaches its maximum at 14:00, or 02:00 pm
(b) The maximum power drawn by the household is 1.83 KW.
Step-by-step explanation:
Extreme points of real functions
Given a real function f(x), we can find the possible maximum or minimum points by computing the first derivative of f, f'(x), and equating it to zero.
The solutions of the resulting equation are the critical points of the function f.
The given function is
[tex]p(t)=-0.007t^2+0.2t+0.4[/tex]
Where t is the number of hours after midnight and p(t) is the power in kilowatts.
Calculate the first derivative and equate to 0:
[tex]p'(t)=-0.014t+0.2=0[/tex]
Solve for t:
[tex]-0.014t=-0.2[/tex]
[tex]t = -0.2 / (-0.014) = 14.29[/tex]
[tex]t\approx 14\ hours[/tex]
(a) The power reaches its maximum at 14:00, or 02:00 pm
To find the maximum value, we use the value of t:
[tex]p(14)=-0.007\cdot 14^2+0.2*14+0.4[/tex]
[tex]p(14)=1.828[/tex]
(b) The maximum power drawn by the household is 1.83 KW.
