Question

The weight of a girl, in pounds, during her first 5 years can be modeled by the function W(t)=0.00001t3−0.006t2+1.004t+6.1 where t is measured in months. What is the rate of change of the girl's weight in pounds per month when she is three and a half years old? Note: Make sure you keep all the digits in your answer. Do not round your answer.

Answer 1

Answer:

Step-by-step explanation:

Since we are asked for the CHANGE of weight we need to build the first derivative of our function W(t).

With $W(t)=0.00001t^{3} -0.006t^{2}+1.004t+6.1$ we get

$W^{`}(t)=0.00003t^{2}-0.012t+1.004$

Remember: $f(x)=x^{n}= > f^{`}(x)=n\cdot x^{n-1}$

Since W(t) is for the first 5 years valid, then W`(t) is also valid for the first 5 years and is the answer to the question (3.5 years is in the Intervall [0,5])