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4th Edition

James Stewart

Publisher: Cengage Learning

ISBN: 9781337687805

Chapter 2.6, Problem 52E

(a)

To determine

The derivative

Expert Solution

**Given:**

The influence of the temperature *T* on the maximum sustainable swimming speed *S* of coho salmon.

**Calculation:**

The maximum sustainable swimming speed *S* is depends on the influence of the temperature *T*.

The maximum sustainable swimming speed *T*.

Note that, the derivative *x*

The derivative *T*.

The instantaneous rate of change is equal to

Here

Thus, the units are centimeter per second 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 15 is passing through the point

The slope of the tangent line to the curve at 15 as follows,

Thus, the slope of the tangent line to the curve at 15 is,

Note that, the slope of the tangent line to the curve at 15 is same

Therefore,

Estimate the value of

Form given Figure, it is observed that the tangent line at 25 is passing through the point

The slope of the tangent line to the curve at 25 as follows,

Thus, the slope of the tangent line to the curve at 25 is,

Note that, the slope of the tangent line to the curve at 25 is same as

Therefore,

The derivative