Question

A keyboarder's speed over a 55​-min interval is given by the following​ function, where Upper W left parenthesis t right parenthesis W (t) is the​ speed, in words per​ minute, at time t.

Upper W left parenthesis t right parenthesis W(t)equals=negative 3 t squared plus 6 t plus 45

​a) Find the speed at the beginning of the interval.

​b) Find the maximum speed and when it occurs.

​c) Find the average speed over the 55​-min interval.

Answer 1

Given W(t) =-3t^2+6t+45

a). The speed beginning of the interval.

i.e at t=0,

W(0)=0+0+45=45

b).We have

W(t) =-3t^2+6t+45 ........... (i)

Differentiate (i) with respect to t

W'(t) =-6t+6

For extremum of W(t), we have W'(t) =0

i.e. t=1

Again Differentiate (i) with respect to t

W''(t) =-6<0

S

So at t=1, maximum value of W(t) occurs.

Maximum of [W(t)] is 48

C).The average speed is

=-2815