Question

Typing Speed The function W(t)=-3.75t^2+30t+40 describes a typist’s speed (in words per minute) over a time interval [0, 5].

a. Find W(0).
b. Find the maximu W value and the time t when it occurs.
c. Find the average speed over [0, 5].

Answer 1

a) 66.25

b) 100

c) 83.75

Explanation:

We are given
`W(t)=-3.75t^2+30t+40`

a)
`W(0) = -3.75+30+40=66.25`

b) Maximum value can be found by taking derivative of W(t) with respect to t.

`(dW(t))/(dt) =-7.5t+30=0`

So, t = 4 is absolute maximum.

Thus, maximum value of W(t) is occured at t = 4.

`-3.75*4^2+30*4+40=100`

c) Average value can be found as follows,

`W_(avg)=(1)/(5-0) \int\limits^5_0 (-3.75t^2+30t+40)dt=\\\\=(1)/(5) (-1.25t^3+15t^2+40t)|^5_0=(418.75)/(5) =83.75`