f(x)=−x3+x2+x
f'(x) = -3x2 + 2x +1
f'' (X) = -6x+2
f'' (X) = 0
x = 1/3
we know that if f''(x) < 0 means it's maximum therefore it's concave down
similarly if f''(x) >0 means it's minimum therefore it's concave Up
f(x) is concave up (- $\infty$ ,1/3)
f(x) is concave down (1/3 , + $\infty$ )
Point of inflection : f(1/3) = 11/27
therefore point of inflection : (1/3 , 11/27)