a. Explanation Given: It is given in the question that function of f(x) is f ( x ) = e x Concept Used: In this we must use the concept of derivatives. Wemust use the formula of lim x → 0 e x − 1 x = 1 . Calculation: The graph of the function f ( x ) = e x is shown in the figure. Notice that the graph crosses the y − axis with a slope of 1 b. To determine Find which type of function is f ( x ) = e x and g ( x ) = x e .Compare the differentiation. c. To determine Find whether the two function in part (b) grows more rapidly when x is large.

15th Edition

ISBN: 9781133109631

Author: Stewart, JAMES, Day, Troy

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 3.3, Problem 2E

To determine

Draw the graph of the function f(x)=ex .Show the facts.

To determine

Find which type of function is f(x)=ex and g(x)=xe .Compare the differentiation.

To determine

Find whether the two function in part (b) grows more rapidly when x is large.

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Chapter 3.3, Problem 1E

Chapter 3.3, Problem 3E

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(A) Find an equation of the tangent line to the graph of f(x)=(4x+1)sin(πx) at the point whose x-coordinate is 1/2.(B) Using logarithmic differentiation, find the derivative off(x)=(e^(-3x) √(2x-5))/(6-5x)^4 .

True or False - In deriving the differentiation rules, the word proof is used instead of the word derivation - the delta method and the definition of the derivative were used in finding the derivatives of functions - If a function has a derivative for a particular value of x, the function is said to be differentiable at that value of x.

f(x) = x2 - 8; x = -1, x = 3.a. Find the derivative of f at x. That is, find f′(x).b. Find the slope of the tangent line to the graph of f at each of the two values of x given to the right of the function.

Chapter 3 Solutions

Biocalculus

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Draw the graph of the function f ( x ) = e x .Show the facts.

Solution Summary: The author illustrates how the graph of the function f(x)=ex crosses the y axis with a slope of 1.

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Draw the graph of the function f(x)=ex .Show the facts.

Find which type of function is f(x)=ex and g(x)=xe .Compare the differentiation.

Find whether the two function in part (b) grows more rapidly when x is large.

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Chapter 3 Solutions