Cartesian Coordinates
Using Cartesian Coordinates we mark a point on a graph by how far along and how far…
Integral Calculus
Gottfried Wilhelm Leibnitz (1646-1716) and Sir Isaac Newton (1643-1727) independently discovered calculus…
Lagrange Multipliers
In the previous section we optimized (i.e. found the absolute extrema) a function…
Finding Maxima and Minima using Derivatives
Where is a function at a high or low point? Calculus can…
Examples on Chain Rule (Differentiation Rules)
Examples on Chain Rule Example 10.8 Find F′(x) if F (x) = √[x2 +1] Solution Take u = g(x)…
Euler’s Homogeneous Function Theorem
Let be a homogeneous function of order so that (1) Then define and . Then (2)(3)(4) Let , then…
Homogeneous Functions
To be Homogeneous a function must pass this test: f(zx,zy) = znf(x,y) In other…
