The tangent line to <em>f(x)</em> at some point <em>x</em> has slope equal to <em>f'(x)</em>, so first compute the derivative of <em>f</em> :
<em>f(x)</em> = -10<em>x</em> ² + 8<em>x</em>
<em>f'(x)</em> = -20<em>x</em> + 8
When <em>x</em> = 9, we have
<em>f</em> (9) = -10•9² + 8•9 = -738
<em>f'</em> (9) = -20•9 + 8 = -172
so the slope is -172.
If you also have to find the equation of the tangent line, use the point-slope formula:
<em>y</em> - (-738) = -172 (<em>x</em> - 9)
<em>y</em> = -172<em>x</em> + 810
