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Related Rates.pptx
- 4. RATE OF CHANGE OF A FUNCTION It is defined as the rate at which one quantity is changing with respect to another quantity.
- 5. AVERAGE RATE OF CHANGE OF A FUNCTION
- 8. OBJECTIVES Define related rates Solve situational problems involving related rates
- 10. POLYAβS FOUR STEP RULE IN PROBLEM SOLVING
- 11. Example 1: If π₯2 + π¦2 = 25 and π π π π = π, find π π π π when π = π.
- 12. Example 2: Assume that a point is moving along the graph ππ + πππ = ππ. When the point is at (βπ, π), its π₯-coordinate is increasing at the rate of 0.4 unit per second. How fast is the y-coordinate changing at that moment? (Note: See Figure 1)
- 13. Example 3: Given two variables π and π which are both differentiable functions of π. They are related by the equation π = ππ β π. Given that π π π π = π, find π π π π when π = π.
- 14. Example 4: Air is being pumped into a spherical balloon at a rate of π πππ /πππ. Determine the rate at which the radius of the balloon is increasing when the diameter of the balloon is ππ ππ.
- 15. Example 5. A 17 ft-ladder is leaning against the building. The foot of the ladder is 8 ft from the base of the building and itβs sliding away from the building at 3 ft/s. a. How fast is the top of the ladder sliding down the wall of the building? b. How fast is the area formed by the ladder changing at this instant? c. Find the rate at which the angle between the ladder and the ground is changing at this instant.
- 16. Example 5. A 17 ft-ladder is leaning against the building. The foot of the ladder is 8 ft from the base of the building and itβs sliding away from the building at 3 ft/s. a. ππ¦ ππ‘ = β 8 5 ππ‘/π ππ b. ππ΄ ππ‘ = 161 10 ππ‘2 /π ππ c. ππ ππ‘ = β 1 5 πππ/π ππ
- 17. GROUP ACTIVITY JIGSAW PUZZLE PRESENTATION
- 18. Instruction: The class will be divided into 6 groups. Then, each group will be assigned to a problem. The group will solve that problem and write the solution in a Manila paper or cartolina. The presentation will follow a Jigsaw Puzzle approach format.