Home
Class 12
MATHS
Draw the graph of the function f(x)=x^(x...

Draw the graph of the function `f(x)=x^(x)`

Text Solution

Verified by Experts

We have `f(x)=x^(x)`
Clearly, the domain of the function is `x gt 0`.
Differentiating we get, `f^(')(x) = x^(x)(1+log_(e)x)`
Also for `x lt 1/e, f^(')(x) lt 0` and for `x gt 1//e, f^(')(x) lt 0`.
Thus, `x=1//e` is the point of minima.
`f(1//e) = (1//e)(1//e)`
Also, `lim_(x to 0) x^(x) =e^(lim_(x to 0)limxlogx) = e^(lim_(x to o)(1//x)/(-1//x^(2)))=e^(lim_(xto0)(-x))=e^(0)=1`
and `lim_(xtoinfty)x^(x)=infty`
From the above discussion, the graph of the function is as shown in the following figure.
Promotional Banner

Topper's Solved these Questions

  • CURVE TRACING

    CENGAGE|Exercise Exercise|24 Videos

  • CROSS PRODUCTS

    CENGAGE|Exercise DPP 2.2|13 Videos

  • DEFINITE INTEGRATION

    CENGAGE|Exercise JEE Advanced Previous Year|38 Videos

Similar Questions

Explore conceptually related problems

Draw the graph of the function: f(x)=|x^(2)-3|x|+2|

Draw the graph of the function f(x)=|x^(2)-4|x|+3| and also find the equation f(x)=a has exactly four distinct real roots.

Draw the graph of the function: 1-x

Draw the graph of the function f(x)=2x-|x|

Draw the graph of the function f(x)=x-|x-x^(2)|,-1<=x<=1 and discuss the continuity or discontinuity of f in the interval -1<=x<=1

Draw the graph of the function f(x)= x- |x-x^(2)|, -1 le x le 1 and find the points of non-differentiability.

Draw the graph of the function: f(x) = {(x," if " x le 0),(x^(2)," if " 0 lt x le 2),(x," if " x gt 2):}