Question

The greatest value of y = (x + 1)^1/3 – (x – 1)^1/3 on [0, 1] is –

• A. 1
• B. 0
• C. ^1/3
• D. None

Answer 1

Answer: (D)

None

Answer 2

y' = $\frac{1}{3(x + 1)^{\frac{2}{3}}}$– $\frac{1}{3(x–1)^{\frac{2}{3}}}$= 0

̃ $\begin{matrix} x = 0 \end{matrix}$

$\left. \ \begin{aligned} & atx = 0,y = (1)^{\frac{1}{3}}–(–1)^{\frac{1}{3}} = 2 \\ & x = 1,y = 2^{\frac{1}{3}} \end{aligned} \right\rbrack$greatest value = 2