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Solving Related Rates Problem with Differentiation and Equations

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Learn how to solve related rates problems using differentiation and equations. Understand how to find the unknown rate using given rates and equations relating variables. Step-by-step guide provided.

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Solving Related Rates Problem with Differentiation and Equations

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  1. Related Rates • There will be a rate you know, say dA/dt =-2. • There will be a rate you want to know, say dB/dt, when… (need to be given some information here, e.g. “when B=4”). • Write an equation relating A and B (using formulas from the flyleaf or similar triangles, etc.), e.g. A2 + B2 = 25. • Differentiate both sides with respect to t: 2A dA/dt + 2B dB/dt =0. • Figure out what all the values are except the rate you want. E.g. here B=4, so from A2 + B2 = 25, it follows that A=3. • Plug these values in and solve for the rate you want: 2*3 * (-2) + 2*4* dB/dt =0, so dB/dt =-2/3.

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