NOTE: MUST BE DIGITALIZED NOT HANDWRITTEN BECAUSE I AM HAVING A HARD TIME SEEING MESSY HANDWRITING

TOPIC: APPLICATION OF DERIVATIVES

Direction: Make a one original problem per application. Show the complete solution. Show the step by step explanation on how to solve it. Follow the instruction carefully. Read the reference material below.

a. Related relates (note: it is forbidden to use the area of ??a circle, volume of a cone and volume of a cylinder)

b. Optimization

REFERENCE MATERIAL (SAMPLE PROBLEM)

Related relates

Optimization 2. in order to make Christmas presents for his family members more personal, Dee decided to make boxes from rectangular pieces of cardboard with 10" x 16" dimensions. He then cuts equal squares from the four " a: 7 corners and folds up the sides. Find the length of the Side of the square that he needs to cut out so that the box will have the laggest golurne ' I . hat la the largest volume? U ; uent + Wet. V: (mi-HA360'1h) (an -uwmwn' :1 7+ Related Rates 3. Gaara lives near the beach and his favorite past time is making shapes and castles with the sand. He usually piles sand at a rate of _6_ _in3m min forming a conical _shape whose height is MW of the base. How fast will the _he_ight_ of _t_he pile increase when the cone _1-1. L [_"I reaChs 10 InchesLIqh'i