I understand how to get the slope (getting the imaginary number, etc) but I've only ever done it when x = 1 or -1. How do I do it when x = -3?
I have the question: y = x^2, while x = -3.
I tried doing it, but I got a slope of 2...
Thanks for any help.
The "two point formula" for slope is (y2- y1)/(x2- x1) where (x1, y1) and (x2, y2) are two points on the curve. Here, y= x^2 so y1= x1^2, y2= x2^2. (y2- y1)/(x2- x1)= (x2^2- x1^2)/(x2- x1). Can you simplify that? (Factor the numerator.)
To find the "derivative of the function and the instaneous rate at they coordinate provided" (they are the same thing), take the limit as x1 goes to x2. Finally set the value of x2 to 3.