A hypothetical square grows so that the length of its diagonals are increasing at a rate of 4 m/min. How fast is the area of the square increasing when the diagonals are 14 m each?
1 Answer
Explanation:
Let the length of one side be
Then By Pythagoras,
And, the Area is,
We are told that
By the chain rule,
Differentiating [2] wrt z (implicitly) gives:
Substituting this into [3] gives us:
So, When
Substituting