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Figure 14 Check Your Understanding 2.2 1. Make a good sketch of the function f(x) near the point where x=2, given that f(2)=5, f'(2)=1, and f(2)= -3. 2. The graph of f(x)= x³ is shown in Fir

Figure 14 Check Your Understanding 2.2 1. Make a good sketch of the function f(x) near the point where x=2, given that f(2)=5, f'(2)=1, and f(2)= -3. 2. The graph of f(x)= x³ is shown in Fir

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter5: Inverse, Exponential, And Logarithmic Functions
Section: Chapter Questions
Problem 18T
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Q1,Q3&Q5 needed to be solved correctly in 1 hour in the order to get positive feedback These are easy questions so solve these please do.all correctly
Y 2. The graph of f(x)= x³ is shown in Fig. 15. Figure 17 (a) (d) y Check Your Understanding 2.2 1. Make a good sketch of the function f(x) near the point where X = 2, given that f(2)= 5, f'(2) = 1, and f(2)= -3. y=a³ వి (b) (e) EXERCISES 2.2 Exercises 1-4 refer to the functions whose graphs are given in Fig. 17. 1. Which functions have a positive first derivative for all x? 2. Which functions have a negative first derivative for all x? 3. Which functions have a positive second derivative for all x? HORTIAL FLOAT AUTO REAL RADIAN MP Ploti Plot2 Plot3 NY108X-X2 Figure 15 (a) Is the function increasing at x = 0? (b) Compute f'(0). (c) Reconcile your answers to parts (a) and (b) with the first derivative rule. Y(Y₁xx x NY UNYA 31 NYE UNYW NY NY Figure 14 (c) (a) (1) x 0 2.2 The First- and Second-Derivative Rules 145 Figure 18 100 HORIAL FLOAT AUTO REAL RADIAN MP Solutions can be found following the section exercises. 3. The graph of y=f'(x) is shown in Fig. 16. Explain why f(x) must have a relative minimum point at x = 3. a (a) Figure 16 a (c) (b) y = f'(x) 3 4. Which functions have a negative second derivative for all x? 5. Which one of the graphs in Fig. 18 could represent a function f(x) for which f(a) > 0, f'(a) = 0, and f"(a) <0? 6. Which one of the graphs in Fig. 18 could represent a f(x) for which f(a) = 0, f'(a) <0, and f"(a) > 0? 20 n Y a (b) 201 a (d) function x +a
Transcribed Image Text:Y 2. The graph of f(x)= x³ is shown in Fig. 15. Figure 17 (a) (d) y Check Your Understanding 2.2 1. Make a good sketch of the function f(x) near the point where X = 2, given that f(2)= 5, f'(2) = 1, and f(2)= -3. y=a³ వి (b) (e) EXERCISES 2.2 Exercises 1-4 refer to the functions whose graphs are given in Fig. 17. 1. Which functions have a positive first derivative for all x? 2. Which functions have a negative first derivative for all x? 3. Which functions have a positive second derivative for all x? HORTIAL FLOAT AUTO REAL RADIAN MP Ploti Plot2 Plot3 NY108X-X2 Figure 15 (a) Is the function increasing at x = 0? (b) Compute f'(0). (c) Reconcile your answers to parts (a) and (b) with the first derivative rule. Y(Y₁xx x NY UNYA 31 NYE UNYW NY NY Figure 14 (c) (a) (1) x 0 2.2 The First- and Second-Derivative Rules 145 Figure 18 100 HORIAL FLOAT AUTO REAL RADIAN MP Solutions can be found following the section exercises. 3. The graph of y=f'(x) is shown in Fig. 16. Explain why f(x) must have a relative minimum point at x = 3. a (a) Figure 16 a (c) (b) y = f'(x) 3 4. Which functions have a negative second derivative for all x? 5. Which one of the graphs in Fig. 18 could represent a function f(x) for which f(a) > 0, f'(a) = 0, and f"(a) <0? 6. Which one of the graphs in Fig. 18 could represent a f(x) for which f(a) = 0, f'(a) <0, and f"(a) > 0? 20 n Y a (b) 201 a (d) function x +a
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