Question

What does \[\frac {dy}{dx}\]​ represent geometrically on a curve y = f(x)?

Options

• The area under the curve at point x

• The slope of the tangent to the curve at point x

• The average value of y over the interval

• The distance between two points on the curve

Answer 1

The slope of the tangent to the curve at point x

Explanation:

When Δx → 0, point B on the curve coincides with point A, and the secant line AB becomes the tangent at A. The ratio \[\frac {Δy}{Δx}\] in this limit gives the slope of that tangent, which is \[\frac {dy}{dx}\].