If f(x) , g(x) and h(x) are three differentiable functions throughout their domains and given that their first derivatives are -
f′(x)<0
g′(x)=0
h′(x)≤0
throughout their domains. Then choose the correct option of monotonically decreasing functions -
If f(x) , g(x) and h(x) are three differentiable functions throughout their domains and given that their first derivatives are -
f′(x)<0
g′(x)=0
h′(x)≤0
throughout their domains. Then choose the correct option of monotonically decreasing functions -
The correct option is D f(x), g(x) & h(x)
We know from the definition that strictly decreasing functions( f’(x) < 0 ) and constant functions (f’(x) = 0 ) are also called monotonically decreasing functions.
The condition for a function being a monotonically decreasing function which is f′(x)≤0 means that either the first derivative should be zero throughout the domain or it should be less than zero or it should be both,that is somewhere f’(x) is zero in the domain somewhere else it is less than zero. So, we can say that all the three functions given are monotonically decreasing
f(x), g(x) & h(x)
We know from the definition that strictly decreasing functions( f’(x) < 0 ) and constant functions (f’(x) = 0 ) are also called monotonically decreasing functions.
The condition for a function being a monotonically decreasing function which is f′(x)≤0 means that either the first derivative should be zero throughout the domain or it should be less than zero or it should be both,that is somewhere f’(x) is zero in the domain somewhere else it is less than zero. So, we can say that all the three functions given are monotonically decreasing
