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Show that f(x)={12 x-13 ,2x^2+5, ifxlt=3...

Show that `f(x)={12 x-13 ,2x^2+5,` `ifxlt=3ifx >3` is differentiable at `x=3` . Also, find `f^(prime)(3)dot`

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LHD=RHD
LHD`=lim_(h->0)(f(3-h)-f(3))/(-h)`
`=lim_(h->0)(12(3-h)-13-12*3+13)/(-h)`
`=lim_(h->0)=(-12h)/(-h)=12`
RHD`=lim_(h->0)(f(3+h)-f(3))/h`
`=(2(3+h)^2+5-23)/h`
`lim_(h->0)(18+12h+h^2-18)/h`
`=12`
...
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RD SHARMA-DIFFERENTIABILITY-Solved Examples And Exercises
  1. Find the values of a and b so that the function f(x)={x^2+3x+a ...

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  2. Show that f(x)={12 x-13 ,2x^2+5, ifxlt=3ifx >3 is differentiable at...

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  3. Show that f(x)=x^(1/3) is not differentiable at x=0.

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  4. Show that f(x)=|x-3| is continuous at x=3.

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  5. Show that the function f(x)={x^m sin(1/x) , 0 ,x != 0,x=0 is different...

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  6. Discuss the continuity and differentiability of the function f(x)=|x...

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  7. Show that the function f defined as follows f(x)={3x-2 , 0ltxl...

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  8. Discuss the continuity and differentiability of f(x)={(x-c)cos(1/(x...

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

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  10. Discuss the continuity and differentiability of f(x)=|log||x|dot

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  11. If f is defined by f(x)=x^2-4x+7, show that f^(prime)(5)=2f^(prime)...

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  12. If f is defined by f(x)=x^2, find f^(prime)(2)dot

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  13. Find the derivative of the function f defined by f(x)=m x+c at x=0.

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  14. Discuss the continuity and differentiability of f(x)=e^(|x|)dot

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  15. If for the functionPhi(x)=lambdax^(2)+7x-4, phi (5) = 97, find lam...

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  16. Examine the continuity f(x)={(3x-2,xlt=0), (x+1,x >0)} a t x=0 .

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  17. The setoff points where the function f(x) given by f(x)=|x-3|cosx is d...

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  18. If f(x)={(1-cosx)/(xsinx),x!=0 and 1/2,x=0 then at x=0,f(x) is (a)c...

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  19. If f(x)={1/(1+e^((1,)/x)),x!=0 0,x=0,t h e nf(x) is continuous as well...

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  20. If f(x)=|3-x|+(3+x), where (x) denotes the least integer greater than ...

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