Home
Class 12
MATHS
Separate the interval of convaity of y =...

Separate the interval of convaity of y =x `log_(e)x-(x^(2))/(2)+(1)/(2)`

Text Solution

Verified by Experts

The correct Answer is:
Concave upward in (0,1)
Concave downward in `(1,oo)`
`y=1+log_(e)x-x`
`rarr y''=(1)/(x)-1=(1-x)/(x)`
`y'' gt for x in (0,1)`
and `y'' lt 0 for x in (1,oo)`
`therefore ` graph is concave upward for x in (0,1) and concave downward for x in (1,o)`
Promotional Banner

Topper's Solved these Questions

  • MONOTONICITY AND MAXIMA MINIMA OF FUNCTIONS

    CENGAGE|Exercise Exercise 6.4|16 Videos

  • MONOTONICITY AND MAXIMA MINIMA OF FUNCTIONS

    CENGAGE|Exercise Exercise 6.5|5 Videos

  • MONOTONICITY AND MAXIMA MINIMA OF FUNCTIONS

    CENGAGE|Exercise Exercise 6.2|10 Videos

  • METHODS OF DIFFERETIATION

    CENGAGE|Exercise Question Bank|13 Videos

  • MONOTONOCITY AND NAXINA-MINIMA OF FUNCTIONS

    CENGAGE|Exercise Comprehension Type|6 Videos

Similar Questions

Explore conceptually related problems

Draw the graph of y=log_(e)(x^(2)-1)

Separate the intervals of monotonocity for the function f(x)=x^2e^(-x)

Draw the graph of y=log_(e)(x+sqrt(x^(2)+1))

Draw the graph of y=(log_(e)x)^(2)

Separate the intervals of monotonocity for the function f(x)=((log)_e x)^2+((log)_e x)

Separate the intervals of monotonocity for the function f(x)=-2x^3-9x^2-12 x+1

Find the interval of the monotonicity of the function f(x)= log_(e)((log_(e)x)/(x))

Draw the graph of y=1/(log_(e)x)

Find the partial derivatives of the functions at the indicated point G (x,y) = e ^(x+3y) log (x ^(2) + y ^(2)), (-1, 1)

If x = 9 is one of the solutions of log_(e)(x^(2)+15a^(2))-log_(e)(a-2)=log_(e)((8ax)/(a-2)) ,then