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Differentiate the following functions. 25. y = 3e² - 7x 27. y = xet 29. y = 8e (1 + 2)² 31. y 33. y DE 2x+4-Sex 4 26. y 28. y=(x²+x+1)e 30. y=(1+e)(1-e') 32. y=x+1 34. y Ve +1

Differentiate the following functions. 25. y = 3e² - 7x 27. y = xet 29. y = 8e (1 + 2)² 31. y 33. y DE 2x+4-Sex 4 26. y 28. y=(x²+x+1)e 30. y=(1+e)(1-e') 32. y=x+1 34. y Ve +1

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter6: The Trigonometric Functions
Section6.6: Additional Trigonometric Graphs
Problem 61E
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10:24 AM Mon Oct 31 G !!!! <O> O 10 En A₁ X INCORPORATING TECHNOLOGY NORMAL FLORT AUTO REAL RADIAN MP 0 (2/3) (*) Figure 7 Check Your Understanding 4.2 1. Solve the following equation for x: ex=e². EXERCISES 4.2 1. Show that 1.947734041. ..0451117611. 1.000000167 3. (a) 4. (a) 5. (a) 3-1 by calculating the slope of the secant line passing h through the points (0, 1) and (h, 3). Take h= .1, .01, and .001. 2. Show that 6. (a) Ix-0 2.7-1 by calculating the slope of the secant line passing h through the points (0, 1) and (h, 2.7"). Take h= .1,.01, and .001. (39) In Exercises 3-6, compute the given derivatives with the help of formulas (1)-(4). (2) 4-(29),-1/2 احد اداری ای یار 14-09/1-² (b) (b) (b) (b) ... plus.pearson.com 99 10. All the techniques we have introduced in previous sections for analyzing functions with the TI-83/84 apply to exponential functions as well. To input an exponential function, press [2nd] [e]. For example, in Fig. 7, we evaluate e2/3, e-2/3, and the derivative of e at x = 0. We emphasize the importance of using parentheses when evaluating e. 4-29-2 429-2 Page 231 استاد اما با این 4- (09/01/ 8. (ex/s Write each expression in the form ex for a suitable constant k. 7. (er. (!) 5. (+)* (=) ₁. e4²+2. e²-2 9. (--)². el-x-²-1 11. (e-3/5x 12. Veel e 231 2. Differentiate y = (x + e) Solve each equation for x. 13. x=20 15. -2 = 8 17. e(x²-1)=0 O 4.2 The Exponential Function e* 231 Solutions can be found following the section exercises. 14. exe² 16. e=1 18. 4e (x²+1)=0 19. Find an equation of the tangent line to the graph of f(x) = e, where x = -1. (Use 1/e= .37.) 29% 3 20. Find the point on the graph of f(x)=e, where the tangent line is parallel to y=x. VV ▾ 21. Use the first and second derivative rules from Section 2.2 to show that the graph of ye has no relative extreme points and is always concave up. 25. y=3e-7x 27. y= xe* 29. y=8e (1 +2e¹)² 31. y= 22. Estimate the slope of e* at x = 0 by calculating the slope of the secant line passing through the points (0, 1) and (h, 2). Take h= .01, .001, and .0001. 33. y= 23. Suppose that A = (a, b) is a point on the graph of e*. What is the slope of the graph of e* at the point A? et - 1 24. Find the slope-point form of the equation of the tangent line to the graph of e at the point (a, e"). Differentiate the following functions. □ 2x+4-5e 4 26. y= 28. y=(x²+x+ 1)e 30. y=(1+e)(1-e¹) x+1 32. y= 34. y= Ve+1 35. The graph of y=x-e has one extreme point. Find its coordinates and decide whether it is a maximum or a mini- mum. (Use the second derivative test.) 36. Find the extreme points on the graph of y=x²e, and decide which one is a maximum and which one is a minimum.
Transcribed Image Text:10:24 AM Mon Oct 31 G !!!! <O> O 10 En A₁ X INCORPORATING TECHNOLOGY NORMAL FLORT AUTO REAL RADIAN MP 0 (2/3) (*) Figure 7 Check Your Understanding 4.2 1. Solve the following equation for x: ex=e². EXERCISES 4.2 1. Show that 1.947734041. ..0451117611. 1.000000167 3. (a) 4. (a) 5. (a) 3-1 by calculating the slope of the secant line passing h through the points (0, 1) and (h, 3). Take h= .1, .01, and .001. 2. Show that 6. (a) Ix-0 2.7-1 by calculating the slope of the secant line passing h through the points (0, 1) and (h, 2.7"). Take h= .1,.01, and .001. (39) In Exercises 3-6, compute the given derivatives with the help of formulas (1)-(4). (2) 4-(29),-1/2 احد اداری ای یار 14-09/1-² (b) (b) (b) (b) ... plus.pearson.com 99 10. All the techniques we have introduced in previous sections for analyzing functions with the TI-83/84 apply to exponential functions as well. To input an exponential function, press [2nd] [e]. For example, in Fig. 7, we evaluate e2/3, e-2/3, and the derivative of e at x = 0. We emphasize the importance of using parentheses when evaluating e. 4-29-2 429-2 Page 231 استاد اما با این 4- (09/01/ 8. (ex/s Write each expression in the form ex for a suitable constant k. 7. (er. (!) 5. (+)* (=) ₁. e4²+2. e²-2 9. (--)². el-x-²-1 11. (e-3/5x 12. Veel e 231 2. Differentiate y = (x + e) Solve each equation for x. 13. x=20 15. -2 = 8 17. e(x²-1)=0 O 4.2 The Exponential Function e* 231 Solutions can be found following the section exercises. 14. exe² 16. e=1 18. 4e (x²+1)=0 19. Find an equation of the tangent line to the graph of f(x) = e, where x = -1. (Use 1/e= .37.) 29% 3 20. Find the point on the graph of f(x)=e, where the tangent line is parallel to y=x. VV ▾ 21. Use the first and second derivative rules from Section 2.2 to show that the graph of ye has no relative extreme points and is always concave up. 25. y=3e-7x 27. y= xe* 29. y=8e (1 +2e¹)² 31. y= 22. Estimate the slope of e* at x = 0 by calculating the slope of the secant line passing through the points (0, 1) and (h, 2). Take h= .01, .001, and .0001. 33. y= 23. Suppose that A = (a, b) is a point on the graph of e*. What is the slope of the graph of e* at the point A? et - 1 24. Find the slope-point form of the equation of the tangent line to the graph of e at the point (a, e"). Differentiate the following functions. □ 2x+4-5e 4 26. y= 28. y=(x²+x+ 1)e 30. y=(1+e)(1-e¹) x+1 32. y= 34. y= Ve+1 35. The graph of y=x-e has one extreme point. Find its coordinates and decide whether it is a maximum or a mini- mum. (Use the second derivative test.) 36. Find the extreme points on the graph of y=x²e, and decide which one is a maximum and which one is a minimum.
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