Let , where is an increasing differentiable function and has a positive root.…

MATHEMATICS · Single correct · CBSE · Mathematics · Introduction to Euclid's Geometry · Introduction to Euclid's Geometry

Problem

Let

F(x)=1+f(x)+(f(x))^2+(f(x))^3

, where

f(x)

is an increasing differentiable function and

f(x)=0

has a positive root. Then (1)

F(x)

is an increasing function (2)

F(0)\leq0

(3)

f(0)\leq-1

(4)

F'(0)>0