Let f x = 3 x 2 - 2 3 + 4 , x ∈ R . Then which of the following statements are true? P : x = 0 is a point of local minima of f Q : x = 2 is a point of inflection of f R : f ' is increasing for x > 2

Step-by-step solution

Given, f x = 3 x 2 - 2 3 + 4 Now on rearranging we get, f x = 81 . 3 x 2 - 2 3 Now differentiating both side we get, f ' x = 81 . 3 x 2 - 2 3 · ln 3 · 3 x 2 - 2 2 · 2 x = 81 × 6 3 x 2 - 2 3 × x 2 - 2 2 ln 3 So by using first derivate test we get x = 0 is point of local minima Now differentiating the function f ' x = 486 · ln 3 ⏟ k 3 x 2 - 2 3 x x 2 - 2 2 ⏟ g x We get, g ' x = 3 x 2 - 2 3 x 2 - 2 2 + x · 3 x 2 - 2 3 · 4 x · x 2 - 2 + x · x 2 -