Find the equation of the tangent line to the curve y = x2 – 2x + 7 w

1.	Find the equation of the tangent line to the curve y = x2 – 2x + 7 which is perpendicular to the line 5y – 15x = 13.
Answer» slope of given line is 3 finding the slope of the tangent by differentiating the curve \(\frac{dy}{dx}=2x-2\) m(tangent) = 2x – 2 since both lines are perpendicular to each other (2x – 2) × 3 = – 1 \(x=\frac{5}{6}\) since this point lies on the curve, we can find y by substituting x \(y=\frac{25}{36}-\frac{10}{6}+7=\frac{217}{36}\) therefore, the equation of the tangent is \(y-\frac{217}{36}=-\frac{1}{3}(x-\frac{5}{6})\)

Find the equation of the tangent line to the curve y = x2 – 2x + 7 which is perpendicular to the line 5y – 15x = 13.

Answer»

slope of given line is 3

finding the slope of the tangent by differentiating the curve

\(\frac{dy}{dx}=2x-2\)

m(tangent) = 2x – 2

since both lines are perpendicular to each other

(2x – 2) × 3 = – 1

\(x=\frac{5}{6}\)

since this point lies on the curve, we can find y by substituting x

\(y=\frac{25}{36}-\frac{10}{6}+7=\frac{217}{36}\)

therefore, the equation of the tangent is

\(y-\frac{217}{36}=-\frac{1}{3}(x-\frac{5}{6})\)