Derivatives in Desmos

Plot f and f′ together

Enter your function as f(x) = …, then add f'(x) or d/dx f(x). Where f′ is positive, f is increasing. Zeros of f′ are candidate extrema — then use the first derivative test by reading the sign chart off the graph.

Tangent line at a point

Let a be a slider. The tangent line is y = f'(a)(x - a) + f(a). Drag a to watch the line ride the curve. This is the best check before you write the point-slope form on paper.

Second derivative / concavity

Graph f''(x). Inflection candidates are zeros of f″ where concavity actually changes. Confirm by looking at f itself: a true inflection is a change from cup-up to cup-down, not just a flat spot.