Explanation It is given that f ( x ) = x 4 + 1 . First let y = f ( x ) To find the inverse of this function f − 1 , solve this equation for x in terms of y . Consider, y = x 4 + 1 x 4 = y − 1 x = y − 1 4 Now, interchange the variables x and y , y = x − 1 4 Hence,

15th Edition

ISBN: 9781305177291

Author: James Stewart, Troy Day

Publisher: Cengage Learning

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Rate of Change

The relation between two quantities which displays how much greater one quantity is than another is called ratio.

Slope

The change in the vertical distances is known as the rise and the change in the horizontal distances is known as the run. So, the rise divided by run is nothing but a slope value. It is calculated with simple algebraic equations as:

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Chapter 1.5, Problem 27E

To determine

To find:inverse function of f where f(x)=x4+1,x≥0 and graph f , f−1 and y=x on the same graph. And check iff and f−1 are reflections about the line y=x .

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Chapter 1.5, Problem 26E

Chapter 1.5, Problem 28E

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(b) Find the (instantaneous) rate of change of y at x = 5. In the previous part, we found the average rate of change for several intervals of decreasing size starting at x = 5. The instantaneous rate of change of fat x = 5 is the limit of the average rate of change over the interval [x, x + h] as h approaches 0. This is given by the derivative in the following limit. lim h→0 - f(x + h) − f(x) h The first step to find this limit is to compute f(x + h). Recall that this means replacing the input variable x with the expression x + h in the rule defining f. f(x + h) = (x + h)² - 5(x+ h) = 2xh+h2_ x² + 2xh + h² 5✔ - 5 )x - 5h Step 4 - The second step for finding the derivative of fat x is to find the difference f(x + h) − f(x). - f(x + h) f(x) = = (x² x² + 2xh + h² - ])- = 2x + h² - 5h ])x-5h) - (x² - 5x) = ]) (2x + h - 5) Macbook Pro

Evaluate the integral using integration by parts. Sx² cos (9x) dx

Let f be defined as follows. y = f(x) = x² - 5x (a) Find the average rate of change of y with respect to x in the following intervals. from x = 4 to x = 5 from x = 4 to x = 4.5 from x = 4 to x = 4.1 (b) Find the (instantaneous) rate of change of y at x = 4. Need Help? Read It Master It

Chapter 1 Solutions

Biocalculus: Calculus For Life Sciences

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inverse function of f where f ( x ) = x 4 + 1 , x ≥ 0 and graph f , f − 1 and y = x on the same graph. And check iff and f − 1 are reflections about the line y = x .

Solution Summary: The author explains that the functionsf and f-1 are reflections about the line y=x.

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To find:inverse function of f where f(x)=x4+1,x≥0 and graph f , f−1 and y=x on the same graph. And check iff and f−1 are reflections about the line y=x .

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Chapter 1 Solutions