Question

Suppose the total profit in hundreds of dollars from selling x items

Answer 1

(a). 7

(b). 5

(c). 4

(d). 3.2

(e). 3.1

Step-by-step explanation

Step 1: for question 'a'

`\begin{gathered} \text{rate of change = }\frac{f(b)\text{ - f(a)}}{b-a} \\ \text{ where b = 4 and a = 2} \\ \text{rate of change = }\frac{\lbrack2(4)^2-5(4)+6\rbrack-\lbrack2(2)^2\text{ - 5(2) + 6\rbrack}}{4\text{ - 2}} \\ \text{ = }\frac{18\text{ - 4}}{2} \\ \text{ = }(14)/(2)\text{ = 7} \end{gathered}`

Step 2: for question 'b'

`\begin{gathered} \text{rate of change = }\frac{f(b)\text{ - f(a)}}{b-a} \\ \text{ where b = 3 and a = 2} \\ \text{rate of change = }\frac{\lbrack2(3)^2-5(3)+6\rbrack-\lbrack2(2)^2\text{ - 5(2) + 6\rbrack}}{3\text{ - 2}} \\ \text{ = }\frac{9\text{ - 4}}{1}\text{ = 5} \end{gathered}`

Step 3: for question 'c'

`\begin{gathered} \text{rate of change = }\frac{\lbrack2(2.5)^2-5(2.5)+6\rbrack-\lbrack2(2)^2\text{ - 5(2) + 6\rbrack}}{2.5\text{ - 2}} \\ \text{ = }\frac{6\text{ - 4}}{0.5}\text{ = }4 \end{gathered}`

Step 4: for question 'd'

`\begin{gathered} \text{rate of change = }\frac{\lbrack2(2.1)^2-5(2.1)+6\rbrack-\lbrack2(2)^2\text{ - 5(2) + 6\rbrack}}{2.1\text{ - 2}} \\ \text{ = }\frac{4.32\text{ - 4}}{0.1}\text{ = }3.2 \end{gathered}`

Step 5: for question 'e'

`\begin{gathered} \text{rate of change = }\frac{\lbrack2(2.05)^2-5(2.05)+6\rbrack-\lbrack2(2)^2\text{ - 5(2) + 6\rbrack}}{2.05\text{ - 2}} \\ \text{ = }\frac{4.155\text{ - 4}}{0.05}\text{ = }3.1 \end{gathered}`