1) The ball's position is described by: s(t) = 4.9t² + 450 We want to find the velocity, which is the 1st-order derivative of the displacement function (I assume this is an introductory calculus class) s'(t) = v(t) = 9.8t We get this by multiplying 4.9 x 2 and reducing the exponent by 1. Now we simply plug 5 in for t. v(5) = 9.8* 5 v(5) = 49m/s
2) Our cost function is C(x) = x² - 10,000 To find the average rate of change between these units, we use this formula: ( C(101) - C(100) ) ÷1 . We find the change in C, and divide by the change in x, which is just one. C(101) = 101² - 10,000 C(101) = 201
C(100) = 100² - 10,000 C(100= 0
C(101) - C(100) = 201 Average rate of change in cost is 201 dollars/ unit between the two points.
