Question: If f(x) = cos $\left( \frac{\pi}{2}\lbrack x\rbrack - x^{3} \right)$, 1 \< x \< 2 where [.] is the...

Question

If f(x) = cos $\left( \frac{\pi}{2}\lbrack x\rbrack - x^{3} \right)$ , 1 < x < 2 where [.] is the greatest integer then f ′( $\sqrt[3]{\pi/2}$ ) is

Answer 1

Q 1 < x < 2 ⇒ [x] = 1 ⇒ f(x) = cos (π/2 –x³)

f ′(x) = – sin (π/2– x³) . (–3x²)

f ′ ((π/2)^1/3) = 0

Question: If f(x) = cos \(\left( \frac{\pi}{2}\lbrack x\rbrack - x^{3} \right)\), 1 \< x \< 2 where [.] is the...