Question

If f(x) = cos$\left\{ \frac{\pi}{2}\lbrack x\rbrack - x^{3} \right\}$, 1 < x < 2, and

[x] = the greatest integer ≤ x, then f´$\left( \sqrt[3]{\frac{\pi}{2}} \right)$ is equal to-

• A. 0
• B. $3\left\{ \frac{\pi}{2} \right\}^{2/3}$
• C. –$3\left\{ \frac{\pi}{2} \right\}^{3/2}$
• D. None

Answer 1

Answer: (A)

0

Answer 2

In x ∈(1, 2) . [x] = 1

so f(x) = cos$\left( \frac{\pi}{2} - x^{3} \right)$ = sin x³

f´(x) = 3x².cos x³

f´$\left( \sqrt[3]{\frac{\pi}{2}} \right)$ = 3.$\left( \frac{\pi}{2} \right)^{2/3}$× cos$\frac{\pi}{2}$ = 0