Explanation Given information: Calculation: From the given graph, we can draw the first derivative graph as Since, at f ( 1 ) the function f ( x ) is decreasing, f ' ( 1 ) < 0 f ' ( 1 ) = − 2 (approximately) Since, at f ( 2 ) the function f ( x ) is decreasing, f ' ( 2 ) < 0 f ' ( 2 ) = − 6 To determine (b) To calculate: The quantities f ' ( 1 ) , f ' ( 2 ) a n d f ' ( 3 ) using the formula f ( x ) = 2 e x − 3 x 2 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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Question

Chapter 3.2, Problem 36P

To determine

(a)

To rank:

The quantities f'(1), f '(2) and f '(3) from smallest to largest.

To determine

(b)

To calculate:

The quantities f'(1), f '(2) and f '(3) using the formula

f(x)=2ex−3x2x

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Chapter 3.2, Problem 35P

Chapter 3.2, Problem 37P

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3.1 Limits 1. If lim f(x)=-6 and lim f(x)=5, then lim f(x). Explain your choice. x+3° x+3* x+3 (a) Is 5 (c) Does not exist (b) is 6 (d) is infinite

1 pts Let F and G be vector fields such that ▼ × F(0, 0, 0) = (0.76, -9.78, 3.29), G(0, 0, 0) = (−3.99, 6.15, 2.94), and G is irrotational. Then sin(5V (F × G)) at (0, 0, 0) is Question 1 -0.246 0.072 -0.934 0.478 -0.914 -0.855 0.710 0.262 .

2. Answer the following questions. (A) [50%] Given the vector field F(x, y, z) = (x²y, e", yz²), verify the differential identity Vx (VF) V(V •F) - V²F (B) [50%] Remark. You are confined to use the differential identities. Let u and v be scalar fields, and F be a vector field given by F = (Vu) x (Vv) (i) Show that F is solenoidal (or incompressible). (ii) Show that G = (uvv – vVu) is a vector potential for F.

Chapter 3 Solutions

Applied Calculus, 6e WileyPLUS + Loose-leaf

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(a) To rank: The quantities f ' ( 1 ) , f ' ( 2 ) a n d f ' ( 3 ) from smallest to largest.

Solution Summary: The author explains how to rank the quantities f'(1),.

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(a)

To rank:

The quantities f'(1), f '(2) and f '(3) from smallest to largest.

(b)

To calculate:

The quantities f'(1), f '(2) and f '(3) using the formula

f(x)=2ex−3x2x

Want to see the full answer?

Chapter 3 Solutions

(a) To rank: The quantities f ' ( 1 ) , f ' ( 2 ) a n d f ' ( 3 ) from smallest to largest.

Solution Summary: The author explains how to rank the quantities f'(1),.

Concept explainers

Videos

(a) To rank: The quantities f'(1), f '(2) and f '(3) from smallest to largest.

(b) To calculate: The quantities f'(1), f '(2) and f '(3) using the formula f(x)=2ex−3x2x

Want to see the full answer?

Chapter 3 Solutions

(a)

To rank:

The quantities f'(1), f '(2) and f '(3) from smallest to largest.

(b)

To calculate:

The quantities f'(1), f '(2) and f '(3) using the formula

f(x)=2ex−3x2x