contestada

y= x2 – 3, P(2,1) find the slope of the curve at point p and a equation of the tangent.

Respuesta :

If y = x² - 3, then the slope of the tangent line at the point (2, 1) is equal to the value of dy/dx when x = 2. We have

y = x² - 3  ==>  dy/dx = 2x

so when x = 2, the slope of the tangent is 4.

This tangent passes through the point (2, 1) on the curve, so it has equation

y - 1 = 4(x - 2)

==>  y = 4x - 7