# The given following function $f(x) = ax + b$ is strictly increasing for all real $x$ if

$\

A) a > 0 \\

B) a < 0 \\

C) a = 0 \\

D) a \leqslant 0 \\

\ $

Answer

Verified

363.6k+ views

Hint: Suppose that a function y=f(x) is a differentiable function. In order for the function to be strictly increasing it is necessary and sufficient that it has to follow a condition where $f'(x) > 0$.

Here the given function is $f(x) = ax + b$.

To find the condition for given increasing function we have to find $f'(x)$

So, if we differentiate the given function $f(x)$ with respective $x$ we get

$f(x) = ax + b$

$f'\left( x \right) = a$

We know that for any increasing function $f'(x)$ should be greater than zero i.e. $f'(x) > 0$.

From the given function we can say that $f'\left( x \right) = a$

So from this we can say that for the given function $f(x) = ax + b$ is strictly increasing function for all real x when$a > 0$, where$f'\left( x \right) = a$.

Here the given function is $f(x) = ax + b$.

To find the condition for given increasing function we have to find $f'(x)$

So, if we differentiate the given function $f(x)$ with respective $x$ we get

$f(x) = ax + b$

$f'\left( x \right) = a$

We know that for any increasing function $f'(x)$ should be greater than zero i.e. $f'(x) > 0$.

From the given function we can say that $f'\left( x \right) = a$

So from this we can say that for the given function $f(x) = ax + b$ is strictly increasing function for all real x when$a > 0$, where$f'\left( x \right) = a$.

Last updated date: 28th Sep 2023

â€¢

Total views: 363.6k

â€¢

Views today: 5.63k

Recently Updated Pages

What do you mean by public facilities

Slogan on Noise Pollution

Paragraph on Friendship

Disadvantages of Advertising

Prepare a Pocket Guide on First Aid for your School

What is the Full Form of ILO, UNICEF and UNESCO

Trending doubts

How do you solve x2 11x + 28 0 using the quadratic class 10 maths CBSE

Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE

Summary of the poem Where the Mind is Without Fear class 8 english CBSE

Difference Between Plant Cell and Animal Cell

What is the basic unit of classification class 11 biology CBSE

Fill the blanks with the suitable prepositions 1 The class 9 english CBSE

One cusec is equal to how many liters class 8 maths CBSE

Differentiate between homogeneous and heterogeneous class 12 chemistry CBSE

Give 10 examples for herbs , shrubs , climbers , creepers