Curve y = 2x – x2, y(x) & y′(x) cut x-axis in M & N number of points respectively, find M + N.

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  • 1 Answer

  • y (x) = 2x – x2

    y? (x) = 2x log 2 – 2x

    M = 3

    N = 2

    M + N = 5

Similar Questions for you

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 )

put t = 1 z t h e n d t = 1 z 2 d z  

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

(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

= [ ( l o g e t ) 2 2 ] 1 x = ( l o g x x ) 2 2

Hence f(e) + f ( 1 e ) = 1 2

V
Vishal Baghel

d y d x = 3 a x 2 2 b x

d y d x | x = 1 = 3 a 2 b = 3

a = 2 b + 3 3 [ 1 , 2 ]

2 b + 3 [ 3 , 6 ]

2 b [ 0 , 3 ]

b [ 0 , 3 2 ]

V
Vishal Baghel

f' (x) = cosx + sinx − k ≤ 0∀x ∈ R
k ≥ √2

V
Vishal Baghel

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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