The Derivative Graph Calculator helps visualize a function together with its derivative so that changes in slope are easier to see. A graph can make relationships between increasing, decreasing, and stationary behavior much clearer than a formula alone.
What the Derivative Graph Shows
For y=f(x), the derivative fβ²(x) gives the slope of the original graph at each x-value. Where fβ²(x) is positive, the original function is increasing; where it is negative, the function is decreasing. Zeros of the derivative can correspond to stationary points.
Using the Calculator
Enter the function in the syntax supported by the calculator and generate the graph. Compare the original curve with its derivative rather than reading either graph in isolation. Pay attention to scale because a narrow viewing window can hide important behavior.
Example
For f(x)=xΒ², the derivative is 2x. The original parabola has a horizontal tangent at x=0, and the derivative graph crosses zero there. To the left of zero, 2x is negative; to the right, it is positive, matching the decreasing-then-increasing behavior of xΒ².
Reading Features
A steep positive section of the original curve corresponds to a large positive derivative, while a steep negative section corresponds to a large negative derivative. A flat section places the derivative near zero.
Practical Check
Use the derivative graph as a visual aid, not as a replacement for the exact derivative. Graph resolution, window limits, and numerical plotting can affect how small or sharp features appear.