35.no 4 do like example given solution INCREASING & DECREASING FUNCTIONS) be a function difforentiable in the open interval (a,b)(x) is an increasing function. (positive slope).1(x) is a decreasing function. (negative slope).( 3).(3,2).(2.).r(x) is increasing1(x) is decreasing1(x) is increasingExample 1:Determine the interval where f (x) = 2 - 3x + 4x is increasing & decreasing.Solution:f(x) increasing, f'(x) 0- 3 + 8x8x 0 33.8f(x) increasing in the intervalf(x) decreasing, f'(x) 0 for all xy =+ ex+1X + 1is an increasing function for all x 2x - 5x is a decreasing function in the interval (-1, 5).7. Find the interval where f (x) is increasingTUTORIAL 3512x - 5. Find the intervals whereGiven a function f(x) = 2x +3x1(x) is increasing and decreasing.2.Given f(x) = 4x + 15x- 18x3.Show that f(x) =Given the function f(x) = (x + 1)(x - 2).Find the interval where f(x) is increasing and decreasing.5xGiven the function f(x) =5.Find the interval where f (x) is increasing or decreasing.6.Given the function f(x) =1 + xFind the interval where f(x) is increasing or decreasing.Given the function f (x) =X - 4Find the interval where f (x) is increasing or decreasing.8.Given the function f (x)X- 2X + 2Find the interval where f(x) is increasing or decreasing.Answers:Increasing (-,-2) U (1,)Decreasing : (-2,1)1.Increasing : (-, -3) u (5.)Increasing: (-,0) u (2,)Decreasing: (0,2)5.2.4.Decreasing: (-, 2) u (2,)Increasing: (-,-1) U (-1, )Decreasing: (-«, 4) U (4.)Increasing: (-,-2) (-2, )

Question

35.no 4 do like example given solution INCREASING & DECREASING FUNCTIONS) be a function difforentiable in the open interval (a,b)(x) is an increasing function. (positive slope).1(x) is a decreasing function. (negative slope).( 3).(3,2).(2.).r(x) is increasing1(x) is decreasing1(x) is increasingExample 1:Determine the interval where f (x) = 2 - 3x + 4x is increasing & decreasing.Solution:f(x) increasing, f'(x) > 0- 3 + 8x8x> 0> 33.8f(x) increasing in the intervalf(x) decreasing, f'(x) < 0< 038-3 + 8xf(x) decreasing in the interval (- o,)Example 2: Show that y =X+ e2x+1is an increasing function for all x.X + 1Solution:y+ e2x+1x + 1dydx(x + 1 )(1) – (1)(x)+ e*+* (2)(x + 1)(x +1)²+ 2e?*+ 1(x + 1.> 0 for all x and 2e2x+1 >0 for all xy =+ ex+1X + 1is an increasing function for all x 2x - 5x is a decreasing function in the interval (-1, 5).7. Find the interval where f (x) is increasingTUTORIAL 3512x - 5. Find the intervals whereGiven a function f(x) = 2x +3x1(x) is increasing and decreasing.2.Given f(x) = 4x + 15x- 18x3.Show that f(x) =Given the function f(x) = (x + 1)(x - 2).Find the interval where f(x) is increasing and decreasing.5xGiven the function f(x) =5.Find the interval where f (x) is increasing or decreasing.6.Given the function f(x) =1 + xFind the interval where f(x) is increasing or decreasing.Given the function f (x) =X - 4Find the interval where f (x) is increasing or decreasing.8.Given the function f (x)X- 2X + 2Find the interval where f(x) is increasing or decreasing.Answers:Increasing (-,-2) U (1,)Decreasing : (-2,1)1.Increasing : (-, -3) u (5.)Increasing: (-,0) u (2,)Decreasing: (0,2)5.2.4.Decreasing: (-, 2) u (2,)Increasing: (-,-1) U (-1, )Decreasing: (-«, 4) U (4.)Increasing: (-,-2) (-2, )

Accepted Answer

The solution of question no 4 is given in the next step.

Given the function f(x) = (x + 1)(x- 2). Find the interval where f(x) is increasing and decreasing.