Question
The length $x$ of a rectangle is decreasing at the rate of $5 \mathrm{~cm} /$ minute and the width $y$ is increasing at the rate of $4 \mathrm{~cm} /$ minute. When $x=8 \mathrm{~cm}$ and $y=6 \mathrm{~cm}$, find the rates of change of (a) the perimeter, and (b) the area of the rectangle.
Step 1
The length $x$ is decreasing at a rate of $5 \, \text{cm/min}$, so $\frac{dx}{dt} = -5$. The width $y$ is increasing at a rate of $4 \, \text{cm/min}$, so $\frac{dy}{dt} = 4$. Show more…
Show all steps
Your feedback will help us improve your experience
Tanishq Gupta and 69 other Calculus 1 / AB educators are ready to help you.
Ask a new question
Labs
Want to see this concept in action?
Explore this concept interactively to see how it behaves as you change inputs.
Key Concepts
Recommended Videos
The length $l$ of a rectangle is decreasing at the rate of $2 \mathrm{cm} / \mathrm{sec}$ while the width $w$ is increasing at the rate of $2 \mathrm{cm} / \mathrm{sec} .$ When $l=12 \mathrm{cm}$ and $w=5 \mathrm{cm},$ find the rates of change of (a) the area, (b) the perimeter, and (c) the lengths of the diagonals of the rectangle. Which of these quantities are decreasing, and which are increasing?
Derivatives
Related Rates
The length $l$ of a rectangle is decreasing at the rate of $2 \mathrm{~cm} / \mathrm{s}$ while the width $w$ is increasing at the rate of $2 \mathrm{~cm} / \mathrm{s}$. When $l=12 \mathrm{~cm}$ and $w=5 \mathrm{~cm}$, find the rates of change of (a) the area, (b) the perimeter, and (c) the lengths of the diagonals of the rectangle. Which of these quantities are decreasing, and which are increasing?
Changing dimensions in a rectangle is decreasing at the rate of 2 $\mathrm{cm} / \mathrm{sec}$ while the width $w$ is increasing at the rate of 2 $\mathrm{cm} / \mathrm{sec} .$ When $l=12 \mathrm{cm}$ and $w=5 \mathrm{cm},$ find the rates of change of (a) the area, (b) the perimeter, and (c) the lengths of the diagonals of the rectangle. Which of these quantities are decreasing, and which are increasing?
Differentiation
Transcript
18,000,000+
Students on Numerade
Trusted by students at 8,000+ universities
Watch the video solution with this free unlock.
EMAIL
PASSWORD