How to Draw a Derivative Graph From a Function Graph TUTORIAL

What if I told you that in that location is a way to take the graph of the derivative and quickly draw the graph of the original function?

Jenn (B.S., M.Ed.) of Calcworkshop® teaching derivative graphs

Jenn, Founder Calcworkshop^®, 15+ Years Feel (Licensed & Certified Teacher)

Well, the secret to understanding a graph lies in properly labelling it and learning how to read it.

But it's best to acquire how through exploration.

Derivative Graph Rules

Beneath are three pairs of graphs. The meridian graph is the original office, f(x), and the lesser graph is the derivative, f'(10).

graph of derivative to original function

Graph Of Derivative To Original Function

What do you lot find near each pair?

If the slope of f(ten) is negative, then the graph of f'(x) volition be beneath the x-centrality.
If the slope of f(10) is positive, and so the graph of f'(ten) will be above the x-centrality.
All relative extrema of f(x) will become 10-intercepts of f'(x).
All points of intersection of f(x) will become relative extrema of f'(10).

Additionally, if f(x) is an odd role, then f'(10) is an even office. And if f(x) is an even office, so f'(x) is an odd function. This means that the derivative will more than likely have i less turn than the original function.

Absurd, right?

So, graphing the derivative when given the original office is all almost approximating the slope.

How To Read Derivative Graphs

Alright, this seems uncomplicated enough, merely what do nosotros do if we are given the derivative graph, and we desire to observe the original part?

So glad you asked!

One time again, you just need to know what to look for!

\begin{equation}
\begin{array}{|l|l|l|}
\hline f^{\prime}(x)>0 & \rightarrow & f(x) \text { is increasing } \\
\hline f^{\prime}(x)<0 & \rightarrow & f(x) \text { is decreasing } \\
\hline f^{\prime number}(x) \text { changes from negative to positive } & \rightarrow & f(x) \text { has a relative minimum } \\
\hline f^{\prime}(x) \text { changes from positive to negative } & \rightarrow & f(x) \text { has a relative maximum } \\
\hline f^{\prime}(x) \text { is increasing } & \rightarrow & f(x) \text { is concave up } \\
\hline f^{\prime}(ten) \text { is decreasing } & \rightarrow & f(x) \text { is concave downward } \\
\hline f^{\prime number}(x) \text { has an extreme value } & \rightarrow & f(x) \text { has a betoken of intersection } \\
\hline
\end{array}
\end{equation}

Permit's make sense of this table with a picture. Once more, the key to agreement how to clarify the graph of the derivative is to marker up the graph, as indicated below.

how to find original function from derivative graph

How To Find Original Function From Derivative Graph

estimated function graph

Estimated Function Graph

With the assistance of numerous examples, we will exist able to plot the derivative of an original function and analyze the original part using the graph of the derivative.

Trust me, it's straightforward, and you'll go the hang of information technology in no time.

Let's become to it!

Video Tutorial westward/ Full Lesson & Detailed Examples (Video)

calcworkshop jenn teaching derivative graphs

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