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Solving Related Rates Problem with Differentiation and Equations

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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