Statement-1: The function f ( x )= ln x is increasing in (0,10) and g ( x )=(1/ x ) is decreasing in (0,10) Statement-2: If a differentiable function increases in the interval (a, b) then its derivative function decreases in the interval (a, b).

Question

Statement-1: The function f ( x )= ln x is increasing in (0,10) and g ( x )=(1/ x ) is decreasing in (0,10) Statement-2: If a differentiable function increases in the interval (a, b) then its derivative function decreases in the interval (a, b). (A) Statement-1 is true, statement- 2 is true and statement-2 is correct explanation for statement- 1 . (B) Statement-1 is true, statement-2 is true and statement-2 is NOT the correct explanation for statement-1. (C) Statement-1 is true, statement-2 is false. (D) Statement-1 is false, statement-2 is true.

Tardigrade Admin · Accepted Answer

Consider the example of f ( x )= e x and f prime( x )= e x both increasing

Q. Statement-1: The function $f (x) = ln x$ is increasing in $(0, 10)$ and $g (x) = \frac{1}{x}$ is decreasing in $(0, 10)$
Statement-2: If a differentiable function increases in the interval $(a, b)$ then its derivative function decreases in the interval $(a, b)$ .

Statement-1 is true, statement- 2 is true and statement-2 is correct explanation for statement- 1 .

Statement-1 is true, statement-2 is true and statement-2 is NOT the correct explanation for statement-1.

Statement-1 is true, statement-2 is false.

Statement-1 is false, statement-2 is true.

Consider the example of $f (x) = e^{x}$ and $f^{'} (x) = e^{x}$ both increasing

Q. Statement-1: The function f(x)=lnx is increasing in (0,10) and g(x)=x1​ is decreasing in (0,10) Statement-2: If a differentiable function increases in the interval (a,b) then its derivative function decreases in the interval (a,b).