If f(x)= \left | (x-4)(x-5) \right |,\: \: then \: \: {f}'(x) =?

  • Option 1)

    -2x+9;\: \: x\epsilon R

  • Option 2)

    2x-9 \: \: if\: \: 4<x<5

  • Option 3)

    -2x+9\: \: if\: \: 4<x<5

  • Option 4)

    None of these

 

Answers (1)

f(x)=\left [ (x^{2}-9x+20) \right ]\\ f(x)=\left\{\begin{matrix} -x^{2}+9x-20&4< x< 5 \\ x^{2}-9x+20 & x< 4\:and\:x> 5 \end{matrix}\right.

f{}'(x)=\left\{\begin{matrix} -2x+9x-20&4< x< 5 \\ 2x-9 & \end{matrix}\right.


Option 1)

-2x+9;\: \: x\epsilon R

This solution is incorrect 

Option 2)

2x-9 \: \: if\: \: 4<x<5

This solution is incorrect 

Option 3)

-2x+9\: \: if\: \: 4<x<5

This solution is correct 

Option 4)

None of these

This solution is incorrect 

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