We can label the width of the rectangle x then the length will be three times bigger: 3x. Area of the rectangle can then be expressed as:
Now, we can find the width when the area is equal to 75cm2:
(technically there is another root -5 but we can ignore it as a side of a rectangle can’t be negative)
That means, that if the area of the rectangle is 75cm2, then the width will be 5cm.
Now, we have “rate of change” in the question, which means we need to apply the derivative. We are asked to find the rate of change of area with respect to width:
Finally, we need to find the rate of change of the area when the width is equal to 5 cm (and the area is equal to 75cm2):
I hope that makes it clear. Let me know if you have more questions.
thank you so much, this really helped!!