1. The Derivative Machine

Select a function to feed into the machine:

Original $f(x)$

$$ x^3 + 2x^2 $$
→
1st Derivative $f'(x)$

Slope

?
→
2nd Derivative $f''(x)$

Concavity

?

Click "Differentiate" to start.

2. Visualizing Coordinates

Move the slider. Observe the Coordinates $(x, y)$ floating on each graph.

$f(x)$ Value 0.00 Height
$f'(x)$ Slope 0.00 Stationary
$f''(x)$ Concavity 0.00 Inflection Point

3. Physics: Step-by-Step Calculation

Function: $s(t) = t^3 - 6t^2 + 9t$. (Time $0 \le t \le 5$)

0m
Max
0.0s

4. Practice (Superscript Notation)

Find the first and second derivatives.

$$ f(x) = 4x^3 + 2x^2 $$
1. First Derivative $f'(x)$
$f'(x) = $
x
$+$
x
2. Second Derivative $f''(x)$
$f''(x) = $
x
$+$
x
(Note: For constant term like $12x^0$, enter power 0)