Question

If f(x) = 3f $\left( \frac{x^{2}}{3} \right)$ + f(3– x²) " x Î(–3, 4) where f"(x) > 0 " x Î (–3, 4), then f(x) is

• A. Increasing in $\left( \frac{3}{2},4 \right)$
• B. Decreasing in $\left( - 3, - \frac{3}{2} \right)$
• C. Increasing in $\left( - \frac{3}{2},0 \right)$
• D. Decreasing in $\left( 0,\frac{3}{2} \right)$

Answer 1

Answer: (A)

Increasing in $\left( \frac{3}{2},4 \right)$

Answer 2

f'(x) = 3f '$\left( \frac{x^{2}}{3} \right)\frac{2x}{3}$ – 2x f '(3 – x²)

= 2x [f ' $\left( \frac{x^{2}}{3} \right)$– f '(3 – x²)]

f '(x) = 0 ̃ $\frac{x^{2}}{3}$ = 3 – x² or x = ± 3/2

f "(x) > 0 ̃ f '(x) is increasing