Question 163209
can someone show me how to do this problem:

Suppose that the speed (in m/sec) of a particle moving 
on the x-axis at time t seconds (t is greater than or equal to 0)
is given by:

V(t) = t^3 - 8t^2 + 15t + 10.

By sketching a graph of V(t), estimate during what time period the speed of the particle is less than 10m/sec.

a. Between about t = 2 and t = 4 seconds
b. Between about t = 4 and t = 6 seconds
c. Between about t = 4 and t = 5 seconds
d. Between about t = 3 and t = 5 seconds

{{{graph(400,400,-2,7,-3,20,(x^3-8x^2+15x+10)*sqrt(x)/sqrt(x))}}}

now draw a green horizontal line through 10 on the t-axis
(shown as the x-0axis):

{{{graph(400,400,-2,7,-3,20,(x^3-8x^2+15x+10)*sqrt(x)/sqrt(x),10)}}}

Draw a black vertical line where the curve starts dropping 
below the green line, and another one at the end of the 
place where it drops below the green line. 

{{{drawing(400,400,-.5,7,-3,20,
graph(400,400,-.5,7,-3,20,(x^3-8x^2+15x+10)*sqrt(x)/sqrt(x),10),
line(3,-4,3,21), line(5,-4,5,21)
)}}}

Notice that the vertical lines crosses the t-axis (actually
here it's the x-axis) at 3 and 5:

Answer: The speed is below 10 m/sec when t is between 3 and 5
seconds.  

Edwin</pre>