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# Applying rules of differentiation

### Application of the derivative

• One of the most important uses of calculus is determining stationary (minimum, maximum, inflection) points, sometimes called turning points.
• If we consider $$y=x^{2}$$, we know that we can find the gradient of the tangent at different values of $$x$$ by substituting into the derivative of the function, which is $$\displaystyle \frac{\mathrm{d}y}{\mathrm{d}x}=2x$$.

Notice at the stationary point, the gradient of the tangent is zero (when $$x=0$$, $$\frac{\mathrm{d}y}{\mathrm{d}x} = 0$$), the progression of the tangents show a minimum turning point.