Question 1179793

Consider the function

 {{{f(x) = -x^2 + 27x - 9 }}}

The slope of the tangent line to {{{f(x)}}} at {{{x = -9}}} is ?

find derivate
 {{{f}}}'{{{(x) = -2x + 27}}}........plug in {{{x = -9}}}
 {{{f}}}'{{{(-9) = -2(-9) + 27}}}
{{{f}}}'{{{(-9) =45}}}

=> slope is {{{45}}}

The value of {{{f(x) }}} at {{{x = -9}}} is ?




 {{{f(-9) = -(-9)^2 + 27(-9) - 9 }}}
{{{f(-9) =-333}}}

=> tangent point:  ({{{-9}}},{{{-333}}})=({{{x[1]}}},{{{y[1]}}})

The {{{y}}}-intercept of the tangent line at {{{x = -9}}} is {{{-333}}}

tangent line will be:

{{{y-y[1]=m(x-x[1])}}}
{{{y-(-333)=45(x-(-9))}}}
{{{y+333=45(x+9)}}}
{{{y+333=45x+405}}}
{{{y=45x+405-333}}}
{{{y = 45 x + 72}}}


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