1 and 5 571Section 127 Higher-Order Dervatives%3DSince y= e+y(the original equation).tain%3D%3Dxp2.xp)-(2- y)(器)dx2(2 y)()Now we express our answer without dy/dx. Since2.2 ydx2(2 – y)?(2 – y)3Now Work Problem 31 4PROBLEMS 12.727. a x+b Jy=c29. xy + y – x = 428. y- 6xy = 430. x² + 2xy + y² = 132. e + e = x² + y²(2)-the derivativeat is, in terms31. y = er+y33. If x + 3x + y² = 4y, find d²y/dx² when x = 0 and y = 0.34. Show that the equationd²y3. y = 8 – x,dx?4. y = -x – xr²,dx?substitutingd'F6. F(q) = In (q + 1),f"(x) + 4f'(x) + 4f(x) = 07. f(x) = x² In x, f"(x)8. y =is satisfied if f (x) = (3x – 5)e-2.35. Find the rate of change of f'(x) if f(x) = (5x – 3)*.%3D36. Find the rate of change of f"(x) if(b)„f• (b)f 6(x),f'X^ = (x)f '0In),1.+ x^9 = (x)f(4) „f 'd – 6^ = (4)f 'II12. y = ear, y"14. y = (3x +7)', y"37. Marginal Cost If c = 0.2q? + 2q + 500 is a cost function,how fast is marginal cost changing when q = 97.357?13. y =2r + 3' dx?I + x15. y =-1'38. Marginal Revenue If p= 400 – 40g – q² is a demandequation, how fast is marginal revenue changing when q = 4?16. y = 2r/2 + (2x)/2, y"x –(2x + 5)(5x - 2)39. If f(x) = x - 6x2 + 5x – 6, determine the values of x forwhich f"(x) = 0.18. y= In17. y = In [x(x +a)], y"%3Dx d'y40. Suppose that e = y e*. (a) Determine dy/dx, and expressyour answer in terms of y only. (b) Determine d²y/dx², andexpress your answer in terms of y only.20. y =%3Der' dx²%3DIn Problems 41 and 42, determine f"(x). Then use your graphingcalculator to find all real roots of f"(x) = 0. Round your answersto two decimal places.21. If y = e2r + er, find%3D22. If y = e2In (x*+), find y" when x = 1.%3DIn Problems 23–32, find y".41. f(x) = 6e* – x³ – 15x²23. x² + 4y² – 16 = 024. x2 - y? = 16%3D42. f(x) =1225. y² = 4x26. 9x² + 16y² = 252.%3D

Question

1 and 5 571Section 127 Higher-Order Dervatives%3DSince y= e+y(the original equation).tain%3D%3Dxp2.xp)-(2- y)(器)dx2(2 y)()Now we express our answer without dy/dx. Since2.2 ydx2(2 – y)?(2 – y)3Now Work Problem 31 4PROBLEMS 12.727. a x+b Jy=c29. xy + y – x = 428. y- 6xy = 430. x² + 2xy + y² = 132. e + e = x² + y²(2)-the derivativeat is, in terms31. y = er+y33. If x + 3x + y² = 4y, find d²y/dx² when x = 0 and y = 0.34. Show that the equationd²y3. y = 8 – x,dx?4. y = -x – xr²,dx?substitutingd'F6. F(q) = In (q + 1),f&#34;(x) + 4f'(x) + 4f(x) = 07. f(x) = x² In x, f&#34;(x)8. y =is satisfied if f (x) = (3x – 5)e-2.35. Find the rate of change of f'(x) if f(x) = (5x – 3)*.%3D36. Find the rate of change of f&#34;(x) if(b)„f• (b)f 6(x),f'X^ = (x)f '0In),1.+ x^9 = (x)f(4) „f 'd – 6^ = (4)f 'II12. y = ear, y&#34;14. y = (3x +7)', y&#34;37. Marginal Cost If c = 0.2q? + 2q + 500 is a cost function,how fast is marginal cost changing when q = 97.357?13. y =2r + 3' dx?I + x15. y =-1'38. Marginal Revenue If p= 400 – 40g – q² is a demandequation, how fast is marginal revenue changing when q = 4?16. y = 2r/2 + (2x)/2, y&#34;x –(2x + 5)(5x - 2)39. If f(x) = x - 6x2 + 5x – 6, determine the values of x forwhich f&#34;(x) = 0.18. y= In17. y = In [x(x +a)], y&#34;%3Dx d'y40. Suppose that e = y e*. (a) Determine dy/dx, and expressyour answer in terms of y only. (b) Determine d²y/dx², andexpress your answer in terms of y only.20. y =%3Der' dx²%3DIn Problems 41 and 42, determine f&#34;(x). Then use your graphingcalculator to find all real roots of f&#34;(x) = 0. Round your answersto two decimal places.21. If y = e2r + er, find%3D22. If y = e2In (x*+), find y&#34; when x = 1.%3DIn Problems 23–32, find y&#34;.41. f(x) = 6e* – x³ – 15x²23. x² + 4y² – 16 = 024. x2 - y? = 16%3D42. f(x) =1225. y² = 4x26. 9x² + 16y² = 252.%3D

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