Chapter 10.1, Problem 60E

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11th Edition

Ronald J. Harshbarger + 1 other

ISBN: 9781305108042

Textbook Problem

** Medication** The number of milligrams

(a) For what *t*-values is *x* increasing?

(b) Find the *t*-value at which *x* is maximum.

(c) Find the maximum value of *x.*

**(a)**

To determine

**To calculate:** The value of *t* where the function is increasing if the function is *x* of a medical in the bloodstream *t* hours after the dose is taken can be modeled as given above.

Explanation

**Given Information:**

The provided function is

**Formula Used:**

To obtain the relative maxima and minima of a function,

1. Find the first derivative of the function.

2. Now set the derivative equal to

3. Evaluate

If

If

**Calculation:**

Consider the provided function,

The critical values are the only values at which the graph can have turning points, the derivative cannot change sign anywhere except at the critical value.

Hence, there will no change in the values of critical values as in the derivative graph.

Take out the first derivative of the function by the power rule,

Put the value of

**(b)**

To determine

**To calculate:** The value of *t* where the *x*-value is maximum if the function is *x* of a medical in the bloodstream *t* hours after the dose is taken can be modeled as given above.

**(c)**

To determine

**To calculate:** The maximum value of *x* if the function is *x* of a medical in the bloodstream *t* hours after the dose is taken can be modeled as given above.

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