If `f(x)=` maximum `{x^3,x^2,1/64} AA x in[0,oo)` then

Options

A. `f(x)={(x^(2)",",0 le x le 1),(x^(3)",", x gt 1):}`
B. `f(x)={((1)/(64)",",0 le x le (1)/(4)),(x^(2)",", (1)/(4) lt x le 1),(x^(3)",", x gt 1):}`
C. `f(x)={((1)/(64)",",0 le x le (1)/(8)),(x^(2)",", (1)/(8) lt x le 1),(x^(3)",", x gt 1):}`
D. `f(x)={((1)/(64)",",0 le x le (1)/(8)),(x^(3)",", x gt 1//8):}`

Answer

C

Explanation

Clearly, from the graph, `f(x)={((1)/(64)",",0 le x le (1)/(8)),(x^(2)",", (1)/(8) lt x le 1),(x^(3)",", x gt 1):}`