Application Of Differentiation Application Of Differentiation
---- to find minimum/maximum value ---- to find a critical point and determine whether the critical point is maximum/ minimum value for a function ---- function f(x) ---- function f(x,y) Minimum/maximum value The maximum or minimum area of a location or shape can be found using differentiation The formula for the location or shape must be known first before finding its maximum/ minimum area. Maximum/minimum value occurs when dy/dx = 0 Know More About Tangent Line Approximation
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Minimum/maximum value Maximum value is determined if d^2/dx^2<0 Minimum value is determined if d^2/dx^2<0 Example :An open top box is to be made as shown in the above diagram. What is the maximum volume of the box? Solution :Step 1 :- Formula for volume of a box is V=long x width x height V=(12-2x)(5x)(x) =60x2 – 10x3 Example :Solution : - Step 2 : Find differentiation for V = 60x2 – 10x3 dv/dx=120x-30x^2 Maximum/minimum value occur when dV/dc = 0 120x – 30x2 = 0, x = 0 , 120 – 30x =0 x=4
x(120 - 30x) = 0 120 = 30x Read More About History Of Rational Numbers
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The differentiation is the subfield of calculus and there are various application of differentiation in real world. The differentiation is very important part of math as it is used in many scientific fields. Differentiation can be defined as the process of finding the derivatives of the functions. Differentiation can be used as a tool to calculate or study the rate of change of a quantity with respect to change in some other quantity. The most common example is calculation of velocity and acceleration.
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