How do you find the slope of the tangent line to the parabola $y = 7 x - x^{2}$ $y=7x-x^2$ at the point (1,6)?

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Answer 1 · 2015-04-13T22:39:24

The derivative is $y'=7-2x$ so the slope is $y'(1)=7-2=5$ .

If you want the equation of the tangent line, just use the fact that $y(1)=6$ to write it as $y=5(x-1)+6=5x+1$ .

In general, the derivative of $y=ax^2+bx+c$ is $y'=2ax+b$ .

How do you find the slope of the tangent line to the parabola y=7x-x^2y=7x−x2y=7x-x^2 at the point (1,6)?