5 Steps to a 5 AP Calculus AB 2019 - William Ma

MA 3972-MA-Book May 8, 2018 13:46

54 STEP 4. Review the Knowledge You Need to Score High

5. Select anx-value in each interval and evaluate the polynomial at that value:

SELECTED FACTOR FACTOR POLYNOMIAL

INTERVAL x-VALUE (x+1) (x−4) (x−4)(x+1)

(−∞,−1) − 2 −− +

(−1, 4) 0 +− −

(4,∞)6++ +

Therefore, the intervals (−∞,−1) and (4,∞) make (x−4)(x+1)>0.

6. Check endpoints: Since the inequalityx^2 − 3 x− 4 ≥0 is greater than or equal to 0, both
   endpointsx=−1 andx=4 are included in the solution.


7. Write the solution: The solution is (−∞,−1]∪[4,∞). (See Figure 5.2-3.)

ToolsF1 TraceF3

MAIN RAD AUTO FUNC

ZoomF2 ReGraphF4 MathF5 DrawF6 F7Pen

[−8, 8] by [−5, 5]

Figure 5.2-3

Note that the inequalityx^2 − 3 x≥4 could have been solved by using a graphing calculator.

Entery 1 =x^2 − 3 xandy 2 =4. The graph ofy 1 is abovey 2 on (−∞,−1) and (4,∞). Since

the inequality is≥, the solution set is (−∞,−1] and [4,∞).

Example 2

Solve the inequalityx^3 − 9 x<0, using a graphing calculator. (See Figure 5.2-4.)

ToolsF1 TraceF3

MAIN RAD AUTO FUNC

ZoomF2 ReGraphF4 MathF5 DrawF6 F7Pen

[−10, 10] by [−15, 15]

Figure 5.2-4