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For positive constants a and b, the force between two atoms in a molecule is given f(r) = −a r2 + b r3 , where r > 0 is the distance between the atoms. note: a and b are upper case letters. (a) find f '(r) = (b) find the critical point for f(r). r = (c) find f ''(r) = (d) find the value of r so that f ''(r) = 0.

Write a program that will compute the volume of ice cream served in a cone. as you can see in the diagram below, the ice cream is served as a hemisphere of frozen deliciousness on top of a cone, which is also packed with frozen deliciousness. thus, the total volume of ice cream sold is the volume of the hemisphere plus the volume of the cone. the example shows an ice cream cone in which the hemisphere and cone have a radius of 10 inches and the cone has a height of 15 inches. your program must instead prompt for these two values, which are taken from the keyboard as integers: • the hemisphere/cone radius in inches, and