Optima of a function We all know that the differentiation of a function is zero at point x if the function is optimum (or saddle point) at x. We will try to see what does that means intuitively and using a graph. For more formulas on calculus check out my other blog. ( Calculus in AI and ML ) Theory: Single Variable Function: The function has optima at x if its first derivative equals 0 at x. We follow the below process to find the maxima or minima of a function. \[\begin{align*} &\text{For function } y=f(x),\\ &\text{1. Evaulate c where } \frac{\mathrm{d} y}{\mathrm{d} x}\mid_{x=c} = f'(c) = 0 \\ &\text{There can be more than one c where} f'(c)=0\\ &\text{2. For each c calculate } \frac{\mathrm{d^2} y}{\mathrm{d} x^2} = f''(c) \\ &\text{if }f''(c) \begin{cases} & <0 \text{ There is Maxima at c} \\ & >0 \text{ There is Minima at c} \\ & =0 \text{ Can't be determined} \end{cases} \end{align*}\] Intuition: Let&#
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