Question

Find an equation for the line tangent to the given curve at the given value of x.

y=x² -x; x=2

Answer 1

The function that describes the curve is

To find the equation of the tangent line, we need the slope of the tangent line and a point on the tangent line.

The slope of the tangent line at x = 2 is the derivative of f(x) at x = 2.

The derivative of f(x) is given by

At x = 2,

The point (2, 2) is a point on the tangent line.

Using slope-point formula, the equation of the line tangent to the given curve at x = 2 is

Hence, the equation of the line tangent to the given curve at x = 2 is y = 3x - 4.