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Show that the fn f given by f(x)= x 3 -3x 2 +4x , (x belongs to R) is strictly increasing .

Show that the fn f given by f(x)= x3-3x2+4x ,        (x belongs to R) is strictly increasing .

Grade:12

2 Answers

sahil
142 Points
3 years ago
See in these type of question first differentiate it and then if the equation obtained after differentiating is positive for all x then it is increasing. So after dy/dx we get 3x^2-6x+4 and it can be written as 3x(x-2)+4 now we see as we take x greater or equal to 2 the equation is positive and also when we take x less than or equal to 0 the equation is also positive. Now the only values of x left is 0
sahil
142 Points
3 years ago
See in these type of question first differentiate it and then if the equation obtained after differentiating is positive for all x then it is increasing. So after dy/dx we get 3x^2-6x+4 and it can be written as 3x(x-2)+4 now we see as we take x greater or equal to 2 the equation is positive and also when we take x less than or equal to 0 the equation is also positive. Now the only values of x left is 0

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