Transcription of 3.2 Higher Order Partial Derivatives
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3.2 Higher Order Partial Derivatives
Higher Order Partial DerivativesIffis a function of several variables, then we can find Higher Order partialsin the following (x,y)is a function of two variables, then f xand f yarealso functions of two variables and their partials can be taken. Hence we candifferentiate them with respect toxandyagain and find, 2f x2, the derivative offtaken twice with respect tox, 2f x y, the derivative offwith respect toyand then with respect tox, 2f y x, the derivative offwith respect toxand then with respect toy, 2f y2, the derivative offtaken twice with respect can carry on and find 3f x y2, which is taking the derivative offfirst withrespect toytwice, and then differentiating with respect tox, etc.
3.4 Maxima and Minima Recall from 1-dimensional calculus, to find the points of maxima and minima of a function, we first find the critical points i.e where the tangent line is horizontal f0(x) = 0. Then (i) If f00(x) > 0 the gradient is increasing and we have a local minimum. (ii) If f00(x) < 0 the gradient is decreasing and we have a local ...
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