"Factored form" is NOT (x- 1)(x+ 1), it is (1- x)(1+ x).meeklobraca said:"Factor 1 - x^2 and see where it is zero, and where positive, and where negative."
Im not sure I know what you mean here. Factored form it is (x-1)(x+1)
Its 0 when x = +-1 , positive for 0<x<1 negative for (-infin,0) (1,infin)?
The first derivative is a mathematical concept that represents the rate of change or slope of a function at a specific point. It is written as f'(x) or dy/dx.
The first derivative is important because it can tell us how a function is changing at any given point. It can also help us find maximum and minimum points, as well as the concavity of a function.
The first derivative can be calculated using the power rule, product rule, quotient rule, or chain rule, depending on the function given. It is important to have a good understanding of basic calculus concepts and rules in order to calculate the first derivative accurately.
The first derivative represents the rate of change of a function, while the second derivative represents the rate of change of the first derivative. In other words, the second derivative tells us how the slope of the function is changing at a specific point.
The first derivative has many applications in real life, such as in physics to calculate velocity and acceleration, in economics to find maximum profit or minimum cost, and in biology to model growth and decay. It is a fundamental concept in understanding and analyzing various natural phenomena.