Find range of y

y=4{x}³-3{x}-1

this will have the same range as :
y = 4x³-3x-1 (for x in [0,1)

the maxima or minima will have to be found for y = 4x³-3x-1 (for x in [0,1)

derivative is zero gives 12x²-3

so x=±1/2

so we need to check the end points and this point

f(0) = -1

f(1) = 0 (this will not reach 0)

f(1/2) = -2

so range will be [-2,0)