Let fff be differentiable on R\mathbb RR with f′(x)>0f'(x)>0f′(x)>0 for all real xxx. Define g(x)=∫0xf(t) dtg(x)=\int_0^x f(t)\,\dd tg(x)=∫0xf(t)dt. P:g is strictly increasing on R.Q:g is convex on R (that is, g′′(x)≥0 for all x).R:g(x)>0 for all x>0.\begin{aligned} P &: g\text{ is strictly increasing on }\mathbb R.\\ Q &: g\text{ is convex on }\mathbb R\text{ (that is, }g''(x)\ge0\text{ for all }x).\\ R &: g(x)>0\text{ for all }x>0. \end{aligned}PQR:g is strictly increasing on R.:g is convex on R (that is, g′′(x)≥0 for all x).:g(x)>0 for all x>0. Which of the following is true? APPP onlyBQQQ onlyCRRR onlyDPPP and QQQ onlyEQQQ and RRR onlyFall of themGnone of them