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The formula $\frac{d}{dx}f(x)=6x^2$ is presented as the exact algebraic counterpart to the graphical observations. It matches the standard power-rule pattern for monomials—multiplying by the exponent and reducing the exponent by one—and perfectly fits the symmetric, U-shaped distribution of the seven manually estimated tangent slopes.

Conditions: Valid for $f(x)=2x^3$ on all real $x$.; No proof of the general power rule is provided within the segment itself.

The formula $\frac{d}{dx}f(x)=6x^2$ is presented as the exact algebraic counterpart to the graphical observations. It matches the standard power-rule pattern for monomials—multiplying by the exponent and reducing the exponent by one—and perfectly fits the symmetric, U-shaped distribution of the seven manually estimated tangent slopes.

Conditions: Valid for $f(x)=2x^3$ on all real $x$.; No proof of the general power rule is provided within the segment itself.