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 \\
\ $
Last updated date: 23rd Mar 2023
•
Total views: 308.4k
•
Views today: 3.87k
Answer
308.4k+ 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$f'\left( x \right) = a$.
Recently Updated Pages
If a spring has a period T and is cut into the n equal class 11 physics CBSE

A planet moves around the sun in nearly circular orbit class 11 physics CBSE

In any triangle AB2 BC4 CA3 and D is the midpoint of class 11 maths JEE_Main

In a Delta ABC 2asin dfracAB+C2 is equal to IIT Screening class 11 maths JEE_Main

If in aDelta ABCangle A 45circ angle C 60circ then class 11 maths JEE_Main

If in a triangle rmABC side a sqrt 3 + 1rmcm and angle class 11 maths JEE_Main

Trending doubts
Difference Between Plant Cell and Animal Cell

Write an application to the principal requesting five class 10 english CBSE

Ray optics is valid when characteristic dimensions class 12 physics CBSE

Give 10 examples for herbs , shrubs , climbers , creepers

Write the 6 fundamental rights of India and explain in detail

Write a letter to the principal requesting him to grant class 10 english CBSE

List out three methods of soil conservation

Fill in the blanks A 1 lakh ten thousand B 1 million class 9 maths CBSE

Epipetalous and syngenesious stamens occur in aSolanaceae class 11 biology CBSE
