Excercise 2.4 Q15,Q33&Q35 needed Please solve all questions in the order to get positive feedback These are easy questions you must have to solve all please By Hans solution needed only 23. ySketch the graphs of the following functions.9. f(x)=x³-6x² + 12x - 610. f(x) = -x³12. f(x)= x³ + 2x² + 4x14. f(x)=2x³ + x-216. f(x)=-3x³-6x²-9x-617. f(x)=1-3x+3x²-x³18. f(x)=x³2x2go19. f(x)=x4-6x²21. f(x)=(x-3)4COPYCheck Your Understanding 2.4Determine whether each of the following functions has an asymp-tote as x gets large. If so, give the equation of the straight line thatis the asymptote.EXERCISES 2.4Find the x-intercepts of the given function.pindosT1. y=x²-3x+12. y = x? +5x+53. y = 2x² + 5x+24. y=4-2x-x²5. y = 4x - 4x²-10-6. y = 3x² + 10x +37. Show that the function f(x)= x³ - 2x² + 5x has no relativeextreme points shod Hames wh8. Show that the function f(x) = -x³ + 2x2 - 6x + 3 is alwaysdecreasing.4ooo ads925. y=+x+1itions of the Derivative² + ² + 220. f(x) = 3x4-6x² + 322. f(x) = (x+2)4 - 1Sketch the graphs of the following functions for x 0.1 1-+-+=xx27. y==+=bauol 2x 528. y = 12 +4-00-129. y = 6√x-xA yol olg(d) Look for possible asymptotes.(1)Examine the formula for f(x). If some terms become insignificant as xgets large, and if the rest of the formula gives the equation of a straightline, then that straight line is an asymptote.(ii) Suppose that there is some point a such that f(x) is defined for x near a,but not at a (for example, 1/x at x = 0). If f(x) gets arbitrarily large (inthe positive or negative sense) as x approaches a, the vertical line x = a isan asymptote for the graph.(e) Complete the sketch.11. f(x)= x³ + 3x + 113. f(x)=513x + 6x²-x³15. f(x)=x³2x² + x24. y=2x1226. y=+ 3x + 1xnota 30. y=[Hint: (1, 0) is an x-intercept.]=√1/2+1/231. f(x)==-2x+1In Exercises 31 and 32, determine which function is the derivativeof the other.31.Solutions can be found following the section exercises.2. f(x)=√x+x 3. f(x)=-=-=-f(x)ang32.Box)g(x)og31veYog ad folg bas33. Find the quadratic function f(x) = ax² + bx+c that goes(through (2,0) and has a local maximum at (0, 1).34. Find the quadratic function f(x) = ax² + bx+c that goesthrough (0, 1) and has a local minimum at (1,-1).35. If f'(a) = 0 and f'(x) is increasing at x = a, explain why f(x)must have a local minimum at x = a. [Hint: Use the first-derivative test.]36. If f'(a)= 0 and f'(x) is decreasing at x = a, explain why f(x)must have a local maximum at x = a.

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Excercise 2.4  Q15,Q33&Q35 needed Please solve all questions in the order to get positive feedback These are easy questions you must have to solve all please  By Hans solution needed only 23. ySketch the graphs of the following functions.9. f(x)=x³-6x² + 12x - 610. f(x) = -x³12. f(x)= x³ + 2x² + 4x14. f(x)=2x³ + x-216. f(x)=-3x³-6x²-9x-617. f(x)=1-3x+3x²-x³18. f(x)=x³2x2go19. f(x)=x4-6x²21. f(x)=(x-3)4COPYCheck Your Understanding 2.4Determine whether each of the following functions has an asymp-tote as x gets large. If so, give the equation of the straight line thatis the asymptote.EXERCISES 2.4Find the x-intercepts of the given function.pindosT1. y=x²-3x+12. y = x? +5x+53. y = 2x² + 5x+24. y=4-2x-x²5. y = 4x - 4x²-10-6. y = 3x² + 10x +37. Show that the function f(x)= x³ - 2x² + 5x has no relativeextreme points shod Hames wh8. Show that the function f(x) = -x³ + 2x2 - 6x + 3 is alwaysdecreasing.4ooo ads925. y=+x+1itions of the Derivative² + ² + 220. f(x) = 3x4-6x² + 322. f(x) = (x+2)4 - 1Sketch the graphs of the following functions for x > 0.1 1-+-+=xx27. y==+=bauol 2x 528. y = 12 +4-00-129. y = 6√x-xA yol olg(d) Look for possible asymptotes.(1)Examine the formula for f(x). If some terms become insignificant as xgets large, and if the rest of the formula gives the equation of a straightline, then that straight line is an asymptote.(ii) Suppose that there is some point a such that f(x) is defined for x near a,but not at a (for example, 1/x at x = 0). If f(x) gets arbitrarily large (inthe positive or negative sense) as x approaches a, the vertical line x = a isan asymptote for the graph.(e) Complete the sketch.11. f(x)= x³ + 3x + 113. f(x)=513x + 6x²-x³15. f(x)=x³2x² + x24. y=2x1226. y=+ 3x + 1xnota 30. y=[Hint: (1, 0) is an x-intercept.]=√1/2+1/231. f(x)==-2x+1In Exercises 31 and 32, determine which function is the derivativeof the other.31.Solutions can be found following the section exercises.2. f(x)=√x+x 3. f(x)=-=-=-f(x)ang32.Box)g(x)og31veYog ad folg bas33. Find the quadratic function f(x) = ax² + bx+c that goes(through (2,0) and has a local maximum at (0, 1).34. Find the quadratic function f(x) = ax² + bx+c that goesthrough (0, 1) and has a local minimum at (1,-1).35. If f'(a) = 0 and f'(x) is increasing at x = a, explain why f(x)must have a local minimum at x = a. [Hint: Use the first-derivative test.]36. If f'(a)= 0 and f'(x) is decreasing at x = a, explain why f(x)must have a local maximum at x = a.

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