is the function f(x)=x^2 increasing on decreasing at x = -1.
can anyone please check my reasoning:
the value of the derivative of the function at x=-1 is -2, so that means the slope of the tangent line to the graph at that is a negative value so the function is decreasing at x = -1.
Correct!
Your reasoning is correct. To determine whether the function f(x) = x^2 is increasing or decreasing at x = -1, we can use the first derivative test.
The first step is to calculate the derivative of the function f(x) = x^2. The derivative of x^2 is 2x.
Next, substitute x = -1 into the derivative equation: 2(-1) = -2. The result -2 represents the slope of the tangent line to the graph of the function at x = -1.
Since the slope -2 is negative, this means the tangent line is decreasing. Therefore, the function f(x) = x^2 is indeed decreasing at x = -1.