Thread: Computing Derivatives with a graph?

1. Computing Derivatives with a graph?

Okay Im REALLY confused with derivatives and how to compute them. THe problem I have is this:
There is a graph in which a straight line crosses -0.25 on the x-axis and 1 on the y-axis. Find f'(1/2).

2. The derivative is basically the slope.

If you are asked to find a derivative of a certain point on the graph, just draw a tangent line to the point, pick 2 points on the tangent line and use the slope formula.

3. How do you find the tangent line?

4. Since you are only given the graph and not the function, just draw the tangent line to whichever point you need to find the derivative for.

5. Im sorry, I appreciate your help but im still confused. sorry if im slow so do i just draw a line on the x-axis at 1/2?

the derivative gives you the formula for the slope. once you find the derivative and plug in the required x-value and that gives you your m in the equation of a line (y = mx + b), you can then use your m and a point the line passes through to get your tangent line. however, that is not the case here. you are required to find a slope, why would you find the tangent line. that's not what they asked for, and you don't need it to find the slope. (the tangent line for a straight line, at any point on the line, is itself, by the way). all you are doing is finding the slope of a line that passes through (-0.25, 0) and (0, 1). the slope (for all points on the straight line) is just given by $\displaystyle m = \frac {y_2 - y_1}{x_2 - x_1}$, and you know what those components are, right?