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

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

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To show that the function \[ f(x) = \begin{cases} 12x - 13 & \text{if } x \leq 3 \\ 2x^2 + 5 & \text{if } x > 3 \end{cases} ...
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RD SHARMA ENGLISH-DIFFERENTIABILITY-All Questions
  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 , ifxlt=3 , 2x^2+5 ifx >3 is differentiable ...

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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 but not differentiable 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 ,, 0ltxle1...

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

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  9. Write an example of a function which is everywhere continuous but f...

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

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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 function varphi(x) = lambdax^2+7x-4 , varphi' (5) = 97, ...

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  16. Is |sinx| differentiable ?What about cos|x|?

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  17. The set of 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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