Since the first derivative of a function represents the rate of change of the function y=f(x) with respect to x, the second derivative represents the rate of change of the function. For example, in ki...Since the first derivative of a function represents the rate of change of the function y=f(x) with respect to x, the second derivative represents the rate of change of the function. For example, in kinematics (the study of motion), the speed of an object (y′) signifies the change of position with respect to time but acceleration (y′′) signifies the rate of change of the speed with respect to time.
You find the slope of the line by dividing the up/down difference in the points by the left/right difference, then you use one of the points and the slope to find the y-intercept. Of course, if we let...You find the slope of the line by dividing the up/down difference in the points by the left/right difference, then you use one of the points and the slope to find the y-intercept. Of course, if we let the point x 1 approach x o then Q will approach P along the graph f and thus the slope of the secant line will gradually approach the slope of the tangent line as x 1 approaches x 0 . Therefore, (1) becomes
