: Criteria for the existence of derivatives.
Investigating the existence of derivatives at specific points.
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Establishing the existence of derivatives at specific points. Methods of Differentiation: : Criteria for the existence of derivatives
Find maxima/minima of (f(x)=x^3-3x^2+4). (f'(x)=3x^2-6x=3x(x-2)). Critical points: (x=0,2). (f''(x)=6x-6). (f''(0)=-6<0 \implies) local max at (x=0), value 4. (f''(2)=6>0 \implies) local min at (x=2), value 0.
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: Geometric applications of derivatives .