The hypotenuse ab of a right triangle abc is 5 ft, and one leg, ac, is decreasing at the rate of 2 ft/sec. the rate, in square feet per second, at which the area is changing when ac = 3 is?

Step-by-step explanation:

Since ABC is a right triangle, at any moment it holds that

Moreover, the area A of the triangle is given by

and we know that the rate of change of the length (AC) is

constant decreasing 2, which may be written using the Leibniz

notation as

.

Using the chain rule and the product rule for derivation, the two

first equations tell us

that

and

Moreover, using the first of the last two equations we get

Now, when (AC)=3, we have that

and

.

Hence, at this moment the rate of change of the area of the triangle is

what graph

step-by-step explanation: