Question

Find value of x for wich f(x)=[x(x-2)]^2 is strictly increasing

Answer 1

A function f(x) is said to be a strictly increasing function on (a,b) if x1<x2⇒f(x1)<f(x2) for all x1,x2∈(a,b)

If x1<x2⇒f(x1)>f(x2) for all x1,x2∈(a,b) then f(x) is said to be strictly decreasing on (a,b)

A function f(x) is said to be increasing on [a,b] if it is increasing (decreasing) on (a,b) and it is increasing (decreasing) at x=a and x=b.

The necessary sufficient condition for a differentiable function defined on (a,b) to be strictly increasing on (a,b) is that f′(x)>0 for all x∈(a,b)

The necessary sufficient condition for a differentiable function defined on (a,b) to be strictly decreasing on (a,b) is that f′(x)<0

Answer 2

Step-by-step explanation:

A function f(x) is said to be a strictly increasing function on (a,b) if x1<x2⇒f(x1)<f(x2) for all x1,x2∈(a,b)

If x1<x2⇒f(x1)>f(x2) for all x1,x2∈(a,b) then f(x) is said to be strictly decreasing on (a,b)

A function f(x) is said to be increasing on [a,b] if it is increasing (decreasing) on (a,b) and it is increasing (decreasing) at x=a and x=b.

The necessary sufficient condition for a differentiable function defined on (a,b) to be strictly increasing on (a,b) is that f′(x)>0 for all x∈(a,b)

The necessary sufficient condition for a differentiable function defined on (a,b) to be strictly decreasing on (a,b) is that f′(x)<0