Drawing a derivative of a function

[dbag123]

Homework Statement

Draw a derivative of a function

Relevant Equations

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Red line being the function and blue an approximation of the derivative. Does it look right?

 

[fresh_42]

Problem Statement: Draw a derivative of a function
Relevant Equations: -

View attachment 243898
Red line being the function and blue an approximation of the derivative. Does it look right?

Almost. I think at the beginning (around $x=\frac{1}{2}$) the curve gets steeper for a moment before it flattens again, so the derivative there should first increase a bit. I think at $3/5$ is an inflection point.

 

[dbag123]

Almost. I think at the beginning (around $x=\frac{1}{2}$) the curve gets steeper for a moment before it flattens again, so the derivative there should first increase a bit. I think at $3/5$ is an inflection point.

Thank you

 

[SammyS]

Problem Statement: Draw a derivative of a function
Relevant Equations: -
(Image removed for this reply)

Red line being the function and blue an approximation of the derivative. Does it look right?

You were to sketch the derivative, ƒ'(x), of the function, the derivative being the slope of the line tangent to
y = ƒ(x) at x assuming the graph of ƒ is given in red.

Looking at the graph:

The derivative is positive at x=0, and appears to increase as x increases from x=0 to somewhere in the neighborhood of x=1, at which location, the derivative is a maximum. From there the derivative decreases to zero at about x=2.5. (At this location the function itself is a maximum.) From here, the derivative continues to decrease, becoming more and more negative for the remainder of the graph.

Notice that near x=0.5 and x=1.5, the derivative is very nearly 1 .
Also, the slope, $\dfrac{f(1.5)-f(0.5)}{1.5 - 0.5}$, of the secant line from x0.5 to x=1.5, is a little bit greater than 1. The derivative attains this value somewhere between x=0.5 and 1.5. (Mean Value Theorem).
Since the derivative increases from x=0 to x=0.5 (and a little beyond), the derivative at x=0 is less than 1.

Your graph of the derivative should reflect these ideas.