​ Let f : R → R be defined as f(x) = -4/3x^3 + 2x^2+3x, x>0 3xe^x, x≤0. Then f is increasing function in the interval (1) (-1/2, 2)

Question

Let f : R → R be defined as

f(x) = \(\begin{cases} -\frac{4}{3}x^3+2x^2+3x, & x>0 \\ 3xe^x, & x\leq0 \end{cases}\)

Then f is increasing function in the interval

(1) (-1/2, 2)

(2) (0,2)

(3) (-1, 3/2)

(4) (–3, –1)

Answer 1

Answer is: (3) (-1, 3/2)

So, in complete domain, f(x) is increasing in (-1, 3/2)