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echo94
The length of a rectangle is increasing at a rate of 4 cm/s and its width is increasing at a rate of 5 cm/s. When the length is 11 cm and the width is 4 cm, how fast is the area of the rectangle increasing?
Related rates: We know: \[ \frac{dl}{dt}=4\\ \frac{dw}{dt}=5 \]So: \[ A=lw\implies\\ A'=l\frac{dw}{dt}+\frac{dl}{dt}w \]So: \[ A'=5l+4w \]We evaluate this at: \[ \frac{dA}{dt}\biggr|_{w=4, l=11}=5(11)+4(4)=71 \] Et voilá.