The graph of function f(x) = x5/20 - x4/12 + 5 has :

Option 1 -

No local extremum, one point of inflection.

Option 2 -

Two local maximum, one local minimum, two point of inflection

Option 3 -

One local maximum, one local minimum, one point of inflection.

Option 4 -

One local maximum, one local minimum, two point of inflection.

0 4 Views | Posted 3 weeks ago
Asked by Shiksha User

  • 1 Answer

  • V

    Answered by

    Vishal Baghel | Contributor-Level 10

    3 weeks ago
    Correct Option - 3


    Detailed Solution:

    f (x) = x? /20 - x? /12 + 5
    f' (x) = x? /4 - x³/3 = x³ (x/4 - 1/3)
    Local maxima at 0, Local minima at 4/3
    f' (x) = x³ - x² = x² (x-1)
    x = 1 point of inflection

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A
alok kumar singh

y (x) = 2x – x2

y? (x) = 2x log 2 – 2x

M = 3

N = 2

M + N = 5

V
Vishal Baghel

y = x3

d y d x = 3 x 2 d y d x | ( t , t 3 ) = 3 t 2

Equation of tangent y – t3 = 3t2 (x – t) 

Let again meet the curve at Q ( t 1 , t 1 3 )

t 1 3 t 3 = 3 t 2 ( t 1 t )

t 1 2 + t t 1 + t 2 = 3 t 2 [ ? t 1 t ]

t 1 2 + t t 1 2 t 2 = 0

=> t1 = -2t

Required ordinate = 2 t 3 + t 1 3 3 = 2 t 3 8 t 3 3 = 2 t 3   

A
alok kumar singh

Given f(X) = 1 x l o g e t ( 1 + t ) d t . . . . . . . . . . . . ( i )  

So   f ( 1 x ) = 1 1 / x λ l o g e t 1 + t d t . . . . . . . . . . . . ( i i )

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(i) + (iii), f(x) + f ( 1 x ) = 1 x ( l o g e t 1 + t + l o g e t t ( 1 + t ) ) d t

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V
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