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4th Edition

James Stewart

Publisher: Cengage Learning

ISBN: 9781337687805

Chapter 2.6, Problem 51E

(a)

To determine

The derivative

Expert Solution

**Given:**

The quantity of oxygen that can dissolve in water depends on the temperature of the water.

**Calculation:**

The quantity of oxygen solubility *S* is depends on the water temperature *T*.

The quantity of oxygen solubility *T*.

Note that, the derivative *x*

The derivative *T*.

The instantaneous rate of change is equal to

Here

Thus, the units are milligrams per liter per centigrade.

Therefore, the unit are

(b)

To determine

**To estimate:** The value of

Expert Solution

Estimate the value of

Form given Figure, it is observed that the tangent line at 16 is passing through the point

The slope of the tangent line to the curve at 16 as follows,

Thus, the slope of the tangent line to the curve at 16 is,

Note that, the slope of the tangent line to the curve at 16 is same

Therefore,

The derivative