For the first problem, find the tangent line to at x= 3. The derivative of is and at x= 3, that is 27. Also is 27. The tangent line is y= 27(x- 3)+ 27. Now let x= 2.9
Do the same with . Find the tangent line to the graph at x= 1 and let x= 1.03.
If a side of a cube is "s", its volume is . The derivative is and, in terms of differentials . You can think of "dV" and "ds" as the errors in V and s. Saying that you want "the volume will be correct to within 3%" means that you want less than .03. "How accurately must the edge of a cube be measured", as a percentage, is .