Table of Contents
What is the derivative of a curve explain?
derivative, in mathematics, the rate of change of a function with respect to a variable. Geometrically, the derivative of a function can be interpreted as the slope of the graph of the function or, more precisely, as the slope of the tangent line at a point.
How do you find the tangent line to a curve at a given point?
1) Find the first derivative of f(x). 2) Plug x value of the indicated point into f ‘(x) to find the slope at x. 3) Plug x value into f(x) to find the y coordinate of the tangent point. 4) Combine the slope from step 2 and point from step 3 using the point-slope formula to find the equation for the tangent line.
Is the tangent to the curve the derivative?
At a given point on a curve, the gradient of the curve is equal to the gradient of the tangent to the curve. The derivative (or gradient function) describes the gradient of a curve at any point on the curve. Similarly, it also describes the gradient of a tangent to a curve at any point on the curve.
What is the derivative of a tangent line?
The derivative of a function gives us the slope of the line tangent to the function at any point on the graph. This can be used to find the equation of that tangent line.
Is the first derivative the slope of the tangent line?
The first derivative of a function is the slope of the tangent line for any point on the function! Therefore, it tells when the function is increasing, decreasing or where it has a horizontal tangent!
What’s the difference between derivative and tangent line?
The derivative is not the same thing as a tangent line. Instead, the derivative is a tool for measuring the slope of the tangent line at any particular point, just like a clock measures times throughout the day. With this in mind, you’ll have no trouble tackling tangent line problems on the AP Calculus exam!