The graph of a red oak tree is approximated by the model: y = -0.003(x)^3 + 0.137(x)^2 + 0.458x - 0.839
Where y is the height of the tree (in feet) and x (2

Question

The graph of a red oak tree is approximated by the model: y = -0.003(x)^3 + 0.137(x)^2 + 0.458x - 0.839 
Where y is the height of the tree (in feet) and x (2 <= t <= 34) is it's age (in years)
a) sketch the graph of y by using the procedure for curve sketching
b) find the age of the tree when its growing most rapidly using calculus and graph
c)find the maximum height of the tree

anonymous · Answer

Hi Amani,
part A)
Start by using a graphing calculator or computer graphing tool such as winplot to graph the function. 
part B)
Take the second derivative and set it equal to zero and solve to find the rate at which the tree is growing the fastest.
part C)  
Take the first derivative and set it equal to zero to find the maximum height of the tree.

anonymous · Answer

Let me know if you still need help.