Quantitative Analysis for Management, 13/e

Key Equations

(M6-1)

$$Y=a+bX$$

Equation of a straight line.

(M6-2)

$$b=\frac{\text{Change} \text{in} Y}{\text{Change} \text{in} X}=\frac{\Delta Y}{\Delta X}=\frac{Y_2-Y_1}{X_2-X_1}$$

Slope of a straight line found from two points.

(M6-3)

$$Y\prime =\frac{dY}{dX}=\underset{\Delta X\to 0}{\text{lim}}\left\{\frac{\Delta Y}{\Delta X}\right\}$$

Definition of derivative.

(M6-4)

$$\text{If} Y=c \text{where} c \text{is} \text{any} \text{constant,} \text{then} Y\prime =0$$

Derivative of a constant function.

(M6-5)

$$\text{If} Y=X^n, \text{then} Y\prime =n{X}^{n-1}$$

Derivative of X raised to a power.

(M6-6)

$$\text{If} Y=c{X}^n, \text{then} Y\prime =cn{X}^{n-1}$$

Derivative of a constant times a function of X.

(M6-7)

$$\text{If} Y=1/X^n, \text{then} Y\prime =-n{X}^{-n-1}=-n/X^{n+1}$$

Derivative of $1/X$ to a power.

(M6-8)

$$\text{If} Y=g\left(x\right)+h\left(x\right), \text{then} Y\prime =g\prime \left(x\right)+h\prime \left(x\right)$$

Derivative of the sum of two functions of X.

(M6-9)

$$\text{If} Y=g\left(x\right)-h\left(x\right), \text{then} Y\prime =g\prime \left(x\right)-h\prime \left(x\right)$$

Derivative of the difference of two functions of X.