If you're seeing this message, it means we're having trouble loading external resources on our website.

If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked.

# Connecting f, f', and f'' graphically

Analyzing three graphs to see which describes the derivative of which other graph.

## Want to join the conversation?

• How can you graph acceleration with only the velocity graph?
• Hi Katelin,
Since acceleration is the derivative of velocity, you can plot the slopes of the velocity graph to find the acceleration graph.
• i keep getting confused with positive/ negative and increasing/ decreasing. i dont get when to use which method?
• A derivative is positive when the original function is increasing, and negative when the original function is decreasing. So you look at where the original function increases and decreases to tell you when the derivative is positive or negative.
• When looking at these graphs, how can you tell when the slope is either positive or negative. I'm having difficulty understanding how to draw the derivative of each line.
• The slope of the function is positive when the line is going up and vise versa. One example at the line is going down so Sal starts his line in the negative side of the graph.
• how was the derivative found in this video?
• Although we were unable to find numerical values of the derivatives of any of these graphs, we can use extreme points of the original function graph (mins and maxes) to roughly plot out where the derivative equals zero (aka crosses the x-axis)
(1 vote)
• At , how did you tell that 3rd function is the derivative of the first function. Would I still be wrong if I say that the 1st function is the derivative of the 3rd function?
(1 vote)
• f' is the derivative of f, and f'' is the second derivative of f, which is the first derivative of f'. Every order of derivative after is just the derivative of the function before that.
• What does the F stand for in graphing? Does it not stand for anything? I have been looking everywhere for an answer.
(1 vote)
• f(x) just means "a function in terms of x" and it is the same as y, except f(x) is a function and must have only 1 y-value for each assigned x-values (in other words it must pass the "line test").
• Assuming that f is a polynomial, can I just pick the graphs of of f, f', and f'' visually by recalling that a derivative of a polynomial will produce an polynomial equation of a 1 lesser degree. That means the roots of f will have the greatest number of roots, then f', and lastly f''.

I this right?
(1 vote)
• It's true that f will have more roots than f' or f'', but they may have any number of real roots, which are the only roots that will be visible in a graph. So the degree alone is not enough information.
• how do you find the derivative of a function?
• There are no points, so we can't find the numerical derivative function.
• It's also easy to rule out the graph on the left as f as the other graphs all have multiple roots. If the tangent slope of the first graph only hits 0 at one spot, so the graph of the derivative should only have 1 root crossing the x-axis.