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If f(x)={x^2+3x+a ,xlt=1b x+2,forx >1 i...

If `f(x)={x^2+3x+a ,xlt=1b x+2,forx >1` is everywhere differentiable, find the values of `aa n dbdot`

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To solve the problem, we need to ensure that the function \( f(x) \) is both continuous and differentiable at \( x = 1 \). The function is defined as: \[ f(x) = \begin{cases} x^2 + 3x + a & \text{if } x \leq 1 \\ bx + 2 & \text{if } x > 1 \end{cases} ...
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RD SHARMA-DIFFERENTIABILITY-Solved Examples And Exercises
  1. Show that the function defined by g" "(x)" "=" "x" "" "[x] is disco...

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  2. Find all points of discontinuity of f, where f is defined by f(x)={2...

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  3. If f(x)={x^2+3x+a ,xlt=1b x+2,forx >1 is everywhere differentiable, f...

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  4. Let f(x)=|x| and g(x)=|x^3|, then (a)f(x)a n dg(x) both are continuou...

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

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  6. Find the values of aa n db so that the function f(x)={x^2+3x+a ,ifxlt=...

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  7. The function f(x)=e^(-|x|) is continuous everywhere but not differenti...

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  8. Discuss the continuity and differentiability of f(x)={1-x,x<1(1-x)(2-...

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  9. Show that the function f(x)={|2x-3|[x]xlt=0 and sin((pix)/2),x>0 is co...

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  10. The set of points where the function f(x)=x|x| is differentiable is ...

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  11. The function f(x)=sin^(-1)(cosx) is (a) . discontinuous at x=0 (b). ...

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  12. If f(x)=|ln|x||, then (a)f(x) is continuous and differentiable f...

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  13. Let f(x)={1/(|x|)for|x|geq1a x^2+bfor|x|<1iff(x) is continuous and dif...

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  14. If f(x) = sqrt(1-(sqrt1-x^2)) , then f(x) is (a)continuous on [-1, ...

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  15. If f(x)=a|sinx|+be^|x|+c|x|^3 and if f(x) is differentiable at x=0 the...

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  16. If f(x)=x^2+(x^2)/(1+x^2)+(x^2)/((1+x^2)^2)++(x^2)/((1+x^2)^n)+ , then...

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  17. If f(x)=|(log)2x|, then f(1^+)=1 (b) f(1^-)=-1 f(1)=1 (c) f^(...

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  18. If f(x) ={(|x+2|)/tan^-1(x+2), x != -2 and 2, x=-2 then f(x) is cont...

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  19. Let f(x)=(x+|x|)|x|dot then, for all x . f is continuous (b) f is diff...

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  20. The function f(x)=e^(-|x|) is continuous everywhere but not differenti...

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