What is the non-negative zero of the function f, where f(1) = 6x^2 – 9x– 6?
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2

Step-by-step explanation:

6x² - 9x - 6 = 0

Factor

(6x + 3)(x - 2) = 0

x = {-1/2, 2}

non-negative zero = 2

1 number

if we use a graphing calculator, there is only one such number that satisfies the conclusion of the mean value theorem, that is, a number such that

where the right-hand side is the average rate of change of f on the interval [0.5,0.75], which is the slope of the secant line.

in the attached graph, the black line is the secant line which has its slope as the average rate of change of f on [0.5,0.75], while the orange line is the only tangent line to the graph of f in the interval that satisfies the mvt conclusion.

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