Calculus question. Has to be derived with the formula f(x) - f(a)/x-a. Picture posted below.

Question

anonymous · Answer

attachment

anonymous · Answer

Estimate using slope of straight lines.

anonymous · Answer

$$\frac{f(x) - f(a)}{x-a} \space = \space \frac{y_2-y_1}{x_2-x_1} \space = \space m, slope.$$

anonymous · Answer

Right, but am I not supposed to find the derivative?

anonymous · Answer

With the derivative formula?

anonymous · Answer

Nope, just estimate it.

anonymous · Answer

The derivative is the slope of the tangent line. The tangent line is the limit of the secant line as the two points (x1,y1), (x2,y2) get closer together, so you can estimate by using straight-line slope of two points which are close together.

anonymous · Answer

I'm kind of confused. You say straight line slope, which would obviously be the lines that are straight next to the curve, but I don't have any points on that line.

anonymous · Answer

|dw:1347758716602:dw|