SOLUTION: i. Evaluate the function f(t) = t^3/3 � 2t^2 &#8722; 45t + 58 for extreme values and classify them. ii. What is the value of t at the point of inflection? Please assist

Click here to see ALL problems on Money Word Problems

Question 1076744: i. Evaluate the function f(t) = t^3/3 � 2t^2 − 45t + 58 for extreme values and classify them.

ii. What is the value of t at the point of inflection?

Please assist
Thank you

Answer by KMST(5328) (Show Source):
You can put this solution on YOUR website!
You have to calculate derivatives.

That derivative function is
negative for
(meaning f(t) decreases in that interval);
it is zero at and
(indicating local extreme values of the function),
and the derivative is positive for any other value
(indicating that f(t) is increasing).
So, f(t) increases with t for ,
reaches a local maximum at ,
decreases until reaching a local minimum at ,
and then increases for .
There is no absolute minimum or maximum.
and
.

For inflection points,
we need the second derivative.

shows you that the inflection point is at
.

SOLUTION: i. Evaluate the function f(t) = t^3/3 � 2t^2 &#8722; 45t + 58 for extreme values and classify them. ii. What is the value of t at the point of inflection? Please assist

SOLUTION: i. Evaluate the function f(t) = t^3/3 � 2t^2 − 45t + 58 for extreme values and classify them. ii. What is the value of t at the point of inflection? Please assist