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

Answer 1

Emma Aldridge

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#.

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Answer 2

Evelyn Agard

To find the slope of the tangent line to the parabola y = 7x - x^2 at the point (1, 6), you differentiate the equation of the parabola with respect to x to find the derivative. Then, you evaluate the derivative at x = 1 to find the slope of the tangent line at that point.

The derivative of y = 7x - x^2 is dy/dx = 7 - 2x.

When x = 1, dy/dx = 7 - 2(1) = 5.

So, the slope of the tangent line to the parabola y = 7x - x^2 at the point (1, 6) is 5.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.