applications of derivative

[Cherry]

Analysis of daily output of a factory shows that, on average, the number of units per hour, y, produced after, t, hours of production is

y = 70t+1/2t^2+t^3

a. Find the critical values for this function.
b. Which critical balus make sense in this particular problem?
c. For whic values of, t, for 0<t<8, is y, increasing?

 

[Guido]

Tell me..

For part b of this question, can you clarify the word "balus"?
What do you mean by this word or is it a word?

 

[tkhunny]

I think "balus" = "values". It makes some sense from a typewriter error sense.

As you are in the calculus section, one must assume we get to use derivatives.

y = 70*t + ½*t^2 + t^3
y' = 70 + t + 3*t^2

70 + t + 3*t^2 = 0, has No Real solutions. Interesting critical values must be at extremes of the Range. As we are talking about real products, t = 0 would be one extreme. As far as an upper bound, that is a bit tougher. Maybe we can go with an 8 hour shift, so t = 8

y'' = t + 6*t, which is positive for all t > 0.

Seems like a rather odd problem. Are you sure you transcribed it correctly?