Using the pencil and paper method a derivative came out to be 600, but using a calculator the derivative came out to be 600.000002. Which value is actually the slope of a secant?
I'm not sure what this means? Help please
Neither do i
Sorry
No way to tell, but I'm betting on the secant. The derivative is the limit of the secant's slope, and the calculator can only approximate that using polynomials of finite precision.
For instance, if y=2x^3, then y' = 6x^2
at x=10, the slope of the tangent is 600
But (f(10+h)-f(10))/h = 600.000002 when h= 1/3 * 10^-8
(2*(10+h)^3 - 2*10^3)/h = 600.000002
So which value would you bet on is the slope of the seacant?
As I said, at x=10, the slope of the tangent is 600
That would mean the other value is the approximation -- the slope of the secant.
When you have a function and you want to find the slope of a secant line, you are essentially finding the average rate of change between two points on the function. This slope is typically calculated using the difference between the function values at those two points, divided by the difference between the x-coordinates of the points.
In this case, you obtained two different values for the derivative, one through the pencil and paper method (600) and the other through a calculator (600.000002). The derivative represents the instantaneous rate of change, or the slope of the tangent line at a specific point, instead of the average rate of change between two points.
To determine which value represents the slope of a secant line, you would need to find two points on the function and calculate the difference in y-coordinates divided by the difference in x-coordinates using those specific points. If the two values you obtained (600 and 600.000002) were calculated using this secant formula, then both values can be considered estimates of the slope of the secant line.
However, if the values were obtained using the derivative formula, then the value of 600 would not be the slope of the secant line, as it represents the instantaneous rate of change instead. In that case, the value of 600.000002 would be a more accurate estimate of the slope of the secant line.