Question

find the stationary points of f(x)=x^5-5x^4+5x^3-10​

Answer 1

Answer:

4

Step-by-step explanation:

The given equation is:

f(x)=x  

5

−5x  

4

+5x  

3

−10

To find the extremum points we differentiate and equate it to zero

⇒f  

′

(x)=5x  

4

−20x  

3

+15x  

2

 

f  

′

(x)=0

⇒5x  

4

−20x  

3

+15x  

2

=0

⇒5x  

2

(x  

2

−4x+3)=0

⇒x=0

⇒x  

2

−4x+3=0

⇒(x−3)(x−1)=0

⇒x=3,1

Now to find whether at the critical points we find a maxima or minima we use the second derivative test.

⇒f  

′′

(x)=20x  

3

−60x  

2

+30x

⇒f  

′′

(0)=0

⇒f  

′′

(3)=20×3  

3

−60×3  

2

+30×3

⇒f  

′′

(3)=1170

⇒f  

′′

(3)>0

⇒f  

′′

(1)=20×1  

3

−60×1  

2

+30×1

⇒f  

′′

(1)=−10

⇒f  

′′

(1)<0

Hence we get a minima at x = 3 and a amxima at x =1. Thus,

p=1 and q=3

⇒p+q=4

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