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If f^' (x)=(-(x^2+5x+1))/(x-3)^2 and f(2) = -5, write the equation of the tangent line to f(x) at x = 2.

Question

Please Help!!! Medal Will Be Rewarded! 	
If f^' (x)=(-(x^2+5x+1))/(x-3)^2 and f(2) = -5, write the equation of the tangent line to f(x) at x = 2.

anonymous · Answer

@cwrw238 @surjithayer

anonymous · Answer

$$find~f'(2)~by~putting~x=2~\inf'(x) this~is~slope~of~line~at~x=2$$
thenfind the eq. of tangent by the formula y-(-5)=f'(2)(x-2)

anonymous · Answer

so use that and find the equation?

anonymous · Answer

or is that the equation?

anonymous · Answer

put the value of f'(2) in this eq. and simplify.

anonymous · Answer

okay so my final answer would be f'(2)=7?

anonymous · Answer

$$f'(2)=\frac{ -\left\{ \left( 2 \right)^{2}+5*2+1 \right\} }{\left( 2-3 \right)^{2} }=\frac{ -15  }{ 1 }=-15$$
eq.of tangent is
$$y-\left( -5 \right)=-15\left( x-2 \right)$$
simplify it.