Home
Class 12
MATHS
Draw the graph of y=(log(e)x)^(2)...

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

Text Solution

Verified by Experts

`y=(log_(e)x)^(2) gt 0` for all `x gt 0`
and when `x to 0, log_(e)x to -infty, therefore (log_(e)(x)^(2) to infty)`
When `x to infty, (log_(e)x)^(2) to infty`
Also for `(dy)/(dx) = 0, 2(log_(e)x)/(x)=0 rArr x=1`, which is clearly the point of minima `y(1)=1`
From these information, we can plot the graph of the function as shown in the following figure.

`y^('')=2(1-log_(e)x)/(x^(2))=0`
`y^('') lt 0` for `x gt e`
`y^('') gt 0` for `0 lt x lt e`
Promotional Banner

Topper's Solved these Questions

  • CURVE TRACING

    CENGAGE PUBLICATION|Exercise EXERCISES|24 Videos

  • CROSS PRODUCTS

    CENGAGE PUBLICATION|Exercise DPP 2.2|13 Videos

  • DEFINITE INTEGRATION

    CENGAGE PUBLICATION|Exercise JEE ADVANCED|38 Videos

Similar Questions

Explore conceptually related problems

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

Draw the graph of y=|log_(e)|x|| .

Draw the graph of y= log_(x)sqrtx

Draw the graph of y=|log_(e)(x+3)| .

Draw the graph of y="log"_(e)(x+3) ,

Draw the graph of y=x+1/x

Draw the graph of y = log_(e) (sin x).

Draw the graph of y=log_(e)3x and compare with y=log_(e)x .

Draw the graph of y=x^(2)+(1)/(x^(2)), x !=0 .

Draw the graph of y = cos^(2)x.