Question

A function f(x) is defined on [a,b]. What should be the condition for the function to be a strictly decreasing function at x = b ?

• A. $f\left(b\right)>f(b-h)$
• B. $f(b-h)>f\left(b\right)$
• C. $f\left(b\right)\ge f(b-h)$
• D. $f(b-h)\ge f\left(b\right)$

Answer 1

The correct option is B

$f(b-h)>f\left(b\right)$

Here, point x =b where we have to discuss the monotonicity of the function is a boundary point. And the function is defined only on the left hand side of the point. So, we’ll be considering only two points $x=b\&x=b-h$ , where h is a positive real number tending to zero and b - h < b . For f(x) to be a strictly decreasing function the condition will be f(b-h) > f(b), because if x2>x2 then f(x1)>f(x2)

=> option b is correct