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Show that f(x)=|x| is not differentiabl...

Show that `f(x)=|x|` is not differentiable at `x=0.`

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To show that the function \( f(x) = |x| \) is not differentiable at \( x = 0 \), we need to investigate the left-hand derivative (LHD) and right-hand derivative (RHD) at that point. ### Step-by-Step Solution: 1. **Define the Function**: The function \( f(x) = |x| \) can be expressed piecewise as: \[ f(x) = ...
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RD SHARMA ENGLISH-DIFFERENTIABILITY-All Questions
  1. If sin^-1 x+sin^-1 y+sin^-1 z=(3pi)/2, then find the value of x^2+y^2+...

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  2. If f(x) = (x^l/x^m)^(l+m) (x^m/x^n)^(m+n) (x^n/x^l)^(n+l), then find f...

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  3. Show that f(x)=|x| is not differentiable at x=0.

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  4. Evaluate : tan(cos^-1(-7/25))

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  5. For what choice of a and b is the function f(x)={x^2,xlt=c and a x+...

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  6. Discuss the differentiability of f(x)=x|x| at x=0

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  7. Show that the function f(x)={ x^2sin(1/x) , when x !=0 and 0 when x=0 ...

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  8. If f(2)=2a n df^(prime)(2)=1, then find (lim)(xvec2)(xf(2)-2f(x))/(x-2...

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  9. If sin^-1 x+sin^-1 y+sin^-1 z=(3pi)/2, then find the value of x^2+y^2+...

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  10. Show that f(x)=|x| is not differentiable at x=0 .

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  11. Show that the function f(x)={x-1\ \ \ ,\ \ \ if\ x<2 \ \ \ \ \ \ \ ...

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  12. Show that the function f(x)={((x^2sin(1/x),if,x!=0),(0,if,x=0)) is dif...

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  13. Show that f(x)=x^2 is differentiable at x=1 and find f^(prime)(1) .

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  14. Show that the function f(x)=|x-1| for all x in R , is not differentia...

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  15. Discuss the differentiability of f(x)=x|x| at x=0 .

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  16. Show that the function f(x)={x \ sin \ 1/x\ \ \ ,\ \ \ \ w h e n\ x!=0...

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  17. Discuss the differentiability of f(x)={x e-(1/(|x|)+1/x),x!=0x ,x=0a ...

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  18. If f(x) is differentiable at x=a , find (lim)(x->a)(x^2f(a)-a^2\ f(x))...

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  19. For what choice of a and b is the function f(x)={x^2\ \ \ ,\ \ \ xlt=c...

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  20. If f(2)=4 and f^(prime)(2)=1 , then find (lim)(x->2)(x\ f(2)-2f\ (x))/...

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