What is the answer for question 3) a. ?

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The given curve is `f(x) = 3x^2 - 5x + 11`

(i) At `x = 2, f(x) = 3*2^2 - 5*2 + 11 = 12 - 10 + 11 = 13`

At `x = 3, f(x) = 3*3^2 - 5*3 + 11 = 27 - 15 + 11 = 23`

**The slope of the secant joining the points** `(2, 13)` and `(3, 23)` is

`(23-13)/(3-2) = 10`

` `

(ii) At `x = 2, f(x) = 3*2^2 - 5*2 + 11 = 12 - 10 + 11 = 13`

At`x = 2.5, f(x) = 3*2.5^2 - 5*2.5 + 11 = 18.75 - 12.5 + 11 = 17.25`

**The slope of the secant joining the points** `(2, 13)` and `(2.5, 17.25)` is `(17.25 - 13)/(2.5 - 2) = 8.5`

(iii) At `x = 2, f(x) = 3*2^2 - 5*2 + 11 = 12 - 10 + 11 = 13`

At `x = 2.1, f(x) = 3*2.1^2 - 5*2.1 + 11 = 13.23 - 10.5 + 11 = 13.73`

**The slope of the secant joining the points** `(2, 13)` and `(2.1, 13.73) ` is `(13.73 - 13)/(2.1 - 2) = 7.3`

(iv) At `x = 2, f(x) = 3*2^2 - 5*2 + 11 = 12 - 10 + 11 = 13`

At `x = 2.01, f(x) = 3*2.01^2 - 5*2.01 + 11 = 12.1203 - 10.05 + 11 = 13.0703`

**The slope of the secant joining the points** `(2, 13)` and `(2.01, 13.0703)` is `(13.0703 - 13)/(2.01 - 2) = 7.03`

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