Using implicit differentiation: Related rate problems

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# Using implicit differentiation: Related rate problems - PowerPoint PPT Presentation

Using implicit differentiation: Related rate problems. Differentiating implicitly with respect to t. Here’s what it looks like:. Differentiating implicitly with respect to t. Try this now:. A problem.

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## Using implicit differentiation: Related rate problems

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1. Using implicit differentiation: Related rate problems

2. Differentiating implicitly with respect to t • Here’s what it looks like:

3. Differentiating implicitly with respect to t • Try this now:

4. A problem Motor oil begins leaking onto the floor from an old can in my garage. On the floor, the oil makes a perfect circle. The surface area of the puddle is increasing at a constant rate of 10 cm2/hr. After two hours (when r = 20), how fast is the radius of the puddle increasing? We’ll use five steps to tackle this: • Write down what you know in terms of derivatives. • Write down what you wantin terms of derivatives. • Write down an equation relating the variables involved. (Remember your geometry!) • Differentiate both sides implicitly with respect to t (time). • Substitute and solve for the missing quantity.

5. What do we know? Motor oil begins leaking onto the floor from an old can in my garage. On the floor, the oil makes a perfect circle. The surface area of the puddle is increasing at a constant rate of 10 cm/hr. After two hours (when r = 20), how fast is the radius of the puddle increasing?

6. What do we need to know? Motor oil begins leaking onto the floor from an old can in my garage. On the floor, the oil makes a perfect circle. The surface area of the puddle is increasing at a constant rate of 10 cm/hr. After two hours (when r = 20), how fast is the radius of the puddle increasing?

7. Write an equation relating the variables. Motor oil begins leaking onto the floor from an old can in my garage. On the floor, the oil makes a perfect circle. The surface area of the puddle is increasing at a constant rate of 10 cm/hr. After two hours (when r = 20), how fast is the radius of the puddle increasing?

8. Differentiate implicitly with respect to t Motor oil begins leaking onto the floor from an old can in my garage. On the floor, the oil makes a perfect circle. The surface area of the puddle is increasing at a constant rate of 10 cm/hr. After two hours (when r = 20), how fast is the radius of the puddle increasing?

9. Substitute and solve for the quantity you want to find. Motor oil begins leaking onto the floor from an old can in my garage. On the floor, the oil makes a perfect circle. The surface area of the puddle is increasing at a constant rate of 10 cm/hr. After two hours (when r = 20), how fast is the radius of the puddle increasing?

10. Steps for solving a related rates problem… • Write down what you know in terms of derivatives. • Write down what you wantin terms of derivatives. • Write down an equation relating the variables involved. (Remember your geometry!) • Differentiate both sides implicitly with respect to t (time). • Substitute and solve for the missing quantity.