Question

Without using a calculator, determine if each each of the following functions is increasing or decresing on the interval x= 1 to x= 2 a. g(x) = 40 – 2 b. f (x) = 3x C. h(x) = 2 - X

Answer 1

a. Increasing

b. Increasing

c. Decreasing

Step-by-step explanation:

Part A (g(x) = 4x – 2)

`\begin{gathered} g(2)=4(2)-2=8-2=6 \\ g(1)=4(1)-2=4-2=2 \\ (g(2)-g(1))/(2-1)=(6-2)/(1) \\ =(4)/(1) \\ =4 \end{gathered}`

g(x) is increasing since its rate of change is positive.

Part B (f(x) = 3x)

`\begin{gathered} f(2)=3(2)=6 \\ f(1)=3(1)=3 \\ (f(2)-f(1))/(2-1)=(6-3)/(1) \\ =(3)/(1) \\ =3 \end{gathered}`

f(x) is increasing since its rate of change is positive.

Part C (h(x) = 2-x)

`\begin{gathered} h(2)=2-2=0 \\ h(1)=2-1=1 \\ (h(2)-h(1))/(2-1)=(0-1)/(1) \\ =(-1)/(1) \\ =-1 \end{gathered}`

h(x) is decreasing since its rate of change is negative.