Some psychologists model a child’s ability to memorize by a function of the form m(t) = tln(t)+1 for 0<t<4, where t is time, measured in years.
Determine when a child’s ability to memorize is highest and when it is lowest.
To find the highest and lowest points of the function, we need to take its derivative and set it equal to zero:
m'(t) = ln(t) + 1
ln(t) + 1 = 0
ln(t) = -1
t = e^-1 ≈ 0.368 (lowest point)
So the lowest point of the function occurs at t = 0.368.
To find the highest point, we need to check the endpoints of the domain:
m(0) = 1 (highest point)
m(4) ≈ 10.9
Therefore, the child's ability to memorize is lowest at around 0.368 years (or 4.4 months) and highest at birth (0 years) or age 4.