The function f : [0, 1] → R given by f(x)=α x^3 has

The correct answer is Option (3) - minimum value -1 when $\alpha=-1$

$f(x)=\alpha x^3$

$f'(x)=3αx^2=0⇒x=0$

when $α=1$

$f(0)=0$

$f(1)=1$

when $α=-1$

$f(0)=0$

$f(1)=-1$

min = -1 for $α=-1$