Explanation Given: f ( x ) = x 5 Calculation: By definition, we calculate f ( x ) = x 5 f ' ( x ) = lim h → 0 h ( x + h ) 5 − x 5 h f ' ( x ) = lim h → 0 [ x 5 + 5 x 4 h + 10 x 3 h 2 + 10 x 2 h 3 + 5 x h 4 + h 5 − x 5 h ] f ' ( x ) =

Applied Calculus, 6e WileyPLUS + Loose-leaf

6th Edition

ISBN: 9781119408901

Author: Deborah Hughes-Hallett, Andrew M. Gleason, Patti Frazer Lock, Daniel E. Flath

Publisher: Wiley (WileyPLUS Products)

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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 3, Problem 7FOT

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The derivative of given function f(x)=x5 using definition of derivative.

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Chapter 3, Problem 6FOT

Chapter 3, Problem 8FOT

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Consider the graphs of y = f(x) and y = g(x) in the given diagram y= f(x). y = g(x) Evaluate (f+g)(2) -5 Determine all for which g(x) < f(x) Determine all for which f(x) +3 = g(x)

I) For what value(s) of x does g(x) = -4? Separate multiple answers with commas as needed. J) Give the interval(s) of such that g(x) > 0. Use the union symbol between multiple intervals. K) Give the interval(s) of such that g(x) <0. Use the union symbol between multiple intervals.

need help on B

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Applied Calculus, 6e WileyPLUS + Loose-leaf

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The derivative of given function f ( x ) = x 5 using definition of derivative.

Solution Summary: The author explains that the derivate of the given function is f(x)=x5.

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The derivative of given function f(x)=x5 using definition of derivative.

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Chapter 3 Solutions

The derivative of given function f ( x ) = x 5 using definition of derivative.

Solution Summary: The author explains that the derivate of the given function is f(x)=x5.

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To find: The derivative of given function f(x)=x5 using definition of derivative.

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Chapter 3 Solutions

To find:

The derivative of given function f(x)=x5 using definition of derivative.