How do you find an equation of the tangent line to the parabola #y=x^2-2x+7# at the point (3,10)?
1 Answer
Jan 5, 2017
Explanation:
The gradient of the tangent to a curve at any particular point is give by the derivative of the curve at that point. The normal is perpendicular to the tangent, so the product of their gradients is
so If
#dy/dx = 2x-2#
When
and
So the tangent we seek passes through
# y-10=4(x-3) #
# :. y-10=4x-12#
# :. y=4x-2#
We can confirm this graphically: