The function f x = 2 x + 3 x 2 3 , x ∈ R , has

The function fx=2x+3x23, x∈R, has
  1. exactly one point of local minima and no point of local maxima
  2. exactly one point of local maxima and no point of local minima
  3. exactly one point of local maxima and exactly one point of local minima
  4. exactly two points of local maxima and exactly one point of local minima

Solution

Given: f(x)=2x+3(x)23

⇒f'x=2+2x-13

⇒f'x=21+1x13

⇒f'x=2x13+1x13

The function changes from positive to negative at x=1 and from negative to positive at x=0

So, the point of local maxima M is at x=-1 and the point of local minima m at x=0

Asked in: JEE Main 2024 (29 Jan Shift 2)

Practice more Applications of Derivatives questions on Aicharya