The tangent line to f(x) at some point x has slope equal to f'(x), so first compute the derivative of f :
f(x) = -10x ² + 8x
f'(x) = -20x + 8
When x = 9, we have
f (9) = -10•9² + 8•9 = -738
f' (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:
y - (-738) = -172 (x - 9)
y = -172x + 810
