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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 :

erturkmemmedli

Answer:

a) 66.25

b) 100

c) 83.75

Step-by-step explanation:

We are given [tex]W(t)=-3.75t^2+30t+40[/tex]

a) [tex]W(0) = -3.75+30+40=66.25[/tex]

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

[tex]\frac{dW(t)}{dt} =-7.5t+30=0[/tex]

So, t = 4 is absolute maximum.

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

[tex]-3.75*4^2+30*4+40=100[/tex]

c) Average value can be found as follows,

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

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