For the function, f(x)=3x^2-5x+11, what is the slope of the secant to the curve in the interval from x=2 to x=3?

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justaguide | College Teacher | (Level 2) Distinguished Educator

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The slope of the secant to the curve f(x) = 3x^2 - 5x + 11 from x=2 to x=3 has to be determined.

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 line joining the points (2, 13) and (3, 23) is (23 - 13)/(3 - 2) = 10

The slope of the secant to the curve f(x)=3x^2-5x+11 from x=2 to x=3 is 10.

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