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].

Answer 1

Answer:

a) 66.25

b) 100

c) 83.75

Step-by-step 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.

$\frac{dW(t)}{dt} =-7.5t+30=0$

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,

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