(a) Apparently you are supposed to find the slopes over the various intervals [a,b]. As always, that is
[f(b)-f(a)]/(b-a)
Just plug in the numbers.
(b) By looking at the way the results approach a single value, that is the estimate of the speed.
It should be 50.28
If an arrow is shot upward on Mars with a speed of 54 m/s, its height in meters t seconds later is given by
y = 54t − 1.86t2
(i) [1, 2](ii) [1, 1.5]
(iii) [1, 1.1]
(iv) [1, 1.01]
(v) [1, 1.001]
(b) Estimate the speed when t = 1.
3 answers
54.14
[f(b)-f(a)]/(b-a)
[(58(2)-1.86(2^2)) - (58(1)-1.86(1^2))]/2-1 = 52.42
[(58(2)-1.86(2^2)) - (58(1)-1.86(1^2))]/2-1 = 52.42
2 answers