Answer
Verified
447.9k+ views
Hint: In order to draw the graph for any equation we need to find the local maxima and local minima and where it touches the x-axis and y-axis. Also take some sets of (x,y) by taking x as(-2,-1,0,1,2) to see how a certain graph is going up or down and also find the inflection points.
Complete step-by-step solution:
Given that the graph is $ y=x^3$
So let us find the values of local minima and maxima of the function $f(x) = x^3$
We know that for a point to be a local maxima or local minima$f'(x)$ must be zero and $f''$ (x) should not be zero
Which implies $f'$(x)=$\dfrac{d}{{dx}}({x^3}) = 3x^2 = 0$ which implies $x=0$
but $f''$ (x) = $\dfrac{{{d^2}}}{{d{x^2}}}({x^3}) = 6x$ should not be zero which implies x should not be zero
This says that there are no local minima or local maxima for the given function.
From the function $f'$(x) =$\dfrac{d}{{dx}}({x^3}) = 3x^2$ we got to know that derivative of the given fuction is always positive, which implies the given function is always increasing function.
At x=0 we got to know that both $f'(x)$ and $f''(x)$ are zero, which states that x = 0 is an inflection point for the given function .
let us take some sets of the given function
They will be $(-2,-8) , (-1,-1) , (0,0) , (1,1) , (2,8)$
So the graph will be as shown below
Note: Don't just plot a few points and think you have the graph. Find all the things related to a graph which can change the certainty of the graph like inflection points local maxima and local minima and the intervals where the graph will be increasing or decreasing and so on…
Complete step-by-step solution:
Given that the graph is $ y=x^3$
So let us find the values of local minima and maxima of the function $f(x) = x^3$
We know that for a point to be a local maxima or local minima$f'(x)$ must be zero and $f''$ (x) should not be zero
Which implies $f'$(x)=$\dfrac{d}{{dx}}({x^3}) = 3x^2 = 0$ which implies $x=0$
but $f''$ (x) = $\dfrac{{{d^2}}}{{d{x^2}}}({x^3}) = 6x$ should not be zero which implies x should not be zero
This says that there are no local minima or local maxima for the given function.
From the function $f'$(x) =$\dfrac{d}{{dx}}({x^3}) = 3x^2$ we got to know that derivative of the given fuction is always positive, which implies the given function is always increasing function.
At x=0 we got to know that both $f'(x)$ and $f''(x)$ are zero, which states that x = 0 is an inflection point for the given function .
let us take some sets of the given function
They will be $(-2,-8) , (-1,-1) , (0,0) , (1,1) , (2,8)$
So the graph will be as shown below
Note: Don't just plot a few points and think you have the graph. Find all the things related to a graph which can change the certainty of the graph like inflection points local maxima and local minima and the intervals where the graph will be increasing or decreasing and so on…
Recently Updated Pages
what is the correct chronological order of the following class 10 social science CBSE
Which of the following was not the actual cause for class 10 social science CBSE
Which of the following statements is not correct A class 10 social science CBSE
Which of the following leaders was not present in the class 10 social science CBSE
Garampani Sanctuary is located at A Diphu Assam B Gangtok class 10 social science CBSE
Which one of the following places is not covered by class 10 social science CBSE
Trending doubts
Which are the Top 10 Largest Countries of the World?
The states of India which do not have an International class 10 social science CBSE
The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths
How do you graph the function fx 4x class 9 maths CBSE
One Metric ton is equal to kg A 10000 B 1000 C 100 class 11 physics CBSE
Difference Between Plant Cell and Animal Cell
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
Why is there a time difference of about 5 hours between class 10 social science CBSE
Name the three parallel ranges of the Himalayas Describe class 9 social science CBSE