Integration is not as easy as differentiation. This is first due to its nature. Finding…

Using Cartesian Coordinates we mark a point on a graph by how far along and how far up it is: They…

Gottfried Wilhelm Leibnitz (1646-1716) and Sir Isaac Newton (1643-1727) independently discovered calculus in the mid-17th…

In the previous section we optimized (i.e. found the absolute extrema) a function on a region…

Where is a function at a high or low point? Calculus can help! A maximum…

Examples on Chain Rule Example 10.8 Find F′(x) if F (x) = √[x2 +1] Solution Take u = g(x) = x2 + 1 and f (u)…

Let  be a homogeneous function of order  so that (1) Then define  and . Then (2)(3)(4) Let , then (5) This can…

To be Homogeneous a function must pass this test: f(zx,zy) = znf(x,y) In other words Homogeneous is when…

Fred has mastered differentiating when a function has only one variable. Somehow, he missed the…