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.
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.
1 answer