16.5. Derivative of Polynomial Functions

Although you can easily find the slope of a linear function by looking at m in y = mx + b, you have to apply derivative rules to find the slope of higher degree polynomials.

To find a derivative, type the expression in parentheses and tap the exponent key (x^) twice.

Examples
For #1-4, find the derivative of each polynomial.

For #5, find the slope and equation of the tangent line to the curve through the point (3, -4)

Calculator solutions
Type each expression as given. Enter the expression in parentheses and take the derivative by tapping the exponent key (x^n) twice.
1) Type: (2x - 4)'

2) Type: (2x^4 - 4x^2 + 2x - 1)'

3) Type: ((3x - 4)^3)'

4) Type: ((3x - 4)^3(2x^3 + 4))'

5) In order to find the equation of the tangent line, we need to find the function's derivative and the tangent line's slope at x = 3. Because the app uses the initial value for x to evaluate consequent expressions, we first enter x = 3.
          Step 1: Type in the value for x
                       Type the following: x = 3
          Step 2: Find the derivative of f(x).
                        Type the following: (x^3 + 2x - 5)'
                        The slope shown is the slope of the function at x = 3 which is 29
          Step 3: Find the equation of the tangent line.
                        y = mx + b      plug (3, -4) and the slope (m = 29) into slope-intercept form
                    -4 = 29*3 + b
                                91 = b       y- intercept
           The equation of the tangent line is y = 29x - 91

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