Answer
424.8k+ views
Hint: A function with a graph that moves downward as it is followed from left to right is known as decreasing function. Differentiate the function and then equate with 0 to find the values.
Complete step-by-step answer:
$f(x)=1-x^3-x^5$
Now we differentiate the function,
$f’(x)=\dfrac{d}{dx} f’(x) =0-3x^2-5x^4$
Now we find the values after differentiating,
$\Rightarrow f’(x) =-3x^2-5x^4$
Now we take constants from the LHS common,
$\Rightarrow f’(x) =-x^2(3+5x^2)$
f’(x) = 0 when x = 0
x = 0 is the only critical point because $3+5x^2 >0 \forall x \in R $
f is decreasing on all the x value $ x \in R $
because f’(x)<0 for all $ x \in R $
Therefore , the correct option is d) all the values of x
Note: We need to differentiate the function and not integrate it. Students often go wrong in this step. Now students need to equate the differentiated equation with 0 to find the values of x. This step is very important as otherwise students would not be able to find the values for x.
Complete step-by-step answer:
$f(x)=1-x^3-x^5$
Now we differentiate the function,
$f’(x)=\dfrac{d}{dx} f’(x) =0-3x^2-5x^4$
Now we find the values after differentiating,
$\Rightarrow f’(x) =-3x^2-5x^4$
Now we take constants from the LHS common,
$\Rightarrow f’(x) =-x^2(3+5x^2)$
f’(x) = 0 when x = 0
x = 0 is the only critical point because $3+5x^2 >0 \forall x \in R $
f is decreasing on all the x value $ x \in R $
because f’(x)<0 for all $ x \in R $
Therefore , the correct option is d) all the values of x
Note: We need to differentiate the function and not integrate it. Students often go wrong in this step. Now students need to equate the differentiated equation with 0 to find the values of x. This step is very important as otherwise students would not be able to find the values for x.
Recently Updated Pages
How many sigma and pi bonds are present in HCequiv class 11 chemistry CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Why Are Noble Gases NonReactive class 11 chemistry CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Let X and Y be the sets of all positive divisors of class 11 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Let x and y be 2 real numbers which satisfy the equations class 11 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Let x 4log 2sqrt 9k 1 + 7 and y dfrac132log 2sqrt5 class 11 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Let x22ax+b20 and x22bx+a20 be two equations Then the class 11 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Trending doubts
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
At which age domestication of animals started A Neolithic class 11 social science CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Which are the Top 10 Largest Countries of the World?
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Give 10 examples for herbs , shrubs , climbers , creepers
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Difference Between Plant Cell and Animal Cell
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Write a letter to the principal requesting him to grant class 10 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Change the following sentences into negative and interrogative class 10 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Fill in the blanks A 1 lakh ten thousand B 1 million class 9 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)