calc homework help

Question

The length of a rectangle is increasing at a rate of 3 cm/s and its width is increasing at a rate of 9 cm/s. When the length is 9 cm and the width is 4 cm, how fast is the area of the rectangle increasing?

Answer 1

Hello Ari,

Let's write down what information you're given:

L = 9 cm

W = 4 cm

dL/dt = 3 cm/s

dW/dt = 9 cm/s

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You're asked to find dA/dt. The units for the answer will be cm²/s

The area of a rectangle is A = LW

Taking the derivative of area with respect to time: dA/dt = d (LW)/dt

You'll use the product rule: dA/dt = (dL/dt)W + L(dW/dt)

Now plug in the numbers accordingly and remember the units will be cm²/s .