Class 12 Mathematics — Chapter 6: APPLICATION OF DERIVATIVES

What you'll learn

• ▸Rate of Change of Quantities
• ▸Related Rates
• ▸Increasing and Decreasing Functions
• ▸Tangents and Normals
• ▸Approximation
• ▸Maxima and Minima
• ▸Marginal Cost and Marginal Revenue

Chapter Summary

--- PAGE 1 --- Chapter 6 APPLICATION OF DERIVATIVES ❖ With the Calculus as a key, Mathematics can be successfully applied to the explanation of the course of Nature." — WHITEHEAD ❖ 6.1 Introduction In Chapter 5, we have learnt how to find derivative of composite functions, inverse trigonometric functions, implicit functions, exponential functions and logarithmic functions. In this chapter, we will study applications of the derivative in various disciplines, e.g., in engineering, science, social science, and many other fields. For instance, we will learn how the derivative can be used (i) to determine rate of change of quantities, (ii) to find the equations of tangent and normal to a curve at a point, (iii) to find turning points on the graph of a function which in turn will help us to locate points at which largest or smallest value (locally) of a function occurs. We will also use derivative to find intervals on which a function is increasing or decreasing. Finally, we use the deriv…

Practice Questions from this Chapter

Tap "Get Solution" on any question to ask our AI tutor.

1. Explain rate of change simply. Get Solution →
2. Show calculus in daily life. Get Solution →
3. Quiz me on derivative applications. Get Solution →
4. According to the text, what does the derivative `dy/dx` represent? Get Solution →
5. What is the term for the rate of change of total cost with respect to the output? Get Solution →
6. What is the term for the rate of change of total revenue with respect to the number of items sold? Get Solution →
7. According to Theorem 1, what condition on the derivative `f'(x)` implies that the function `f` is decreasing in `[a,b]`? Get Solution →
8. As noted on page 3, what does a positive value of `dy/dx` indicate? Get Solution →

Did you know?

• 💡 Isaac Newton invented calculus partly to predict how planets move.
• 💡 The fastest rate of change in human growth happens before birth.
• 💡 Calculus helps engineers design safe bridges and tall skyscrapers.
• 💡 GPS devices use calculus to calculate your exact speed and position.
• 💡 Economists use derivatives to find the best price for products to maximize profit.

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