. He was kind-hearted, unselfish, and always willing to give anything that he had to his companions.
(a)
We have been given an equation
. Upon taking derivative of this equation with respect to x on both the sides, we get:

(b)
In order to write the equation of tangent line, we need to find the slope of the line. We know that point (3,11) lies on the graph. Therefore, we write the slope of the tangent as:

Therefore, equation of tangent line is:

(c)
We know that slope of tangent is given as
. The tangent will be vertical when denominator of slope is zero, that is:

The correct answer to the question is to report
Basically, Benedict's test identifies the existence of aldehydes and alpha-hydroxy-ketones, also by hemiacetal, as well as those that take place in specific ketoses. Therefore, it is an alpha-hydroxy-ketone even if the ketose fructose is not strictly a reducing sugar, and provides a positive test since it is transformed into the mannose and aldoses glucose by the base inside the reagent.