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The graph of the function is shown to y=(12)/(13)(x²-25)²/³

User Dmorlock
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Final answer:

The question requires analysis of a function's positive value and decreasing positive slope at x=3. None of the given options, y=13x or y=x², completely satisfy these conditions as the first has a constant slope and the latter has an increasing slope with increasing x.

Step-by-step explanation:

The question pertains to the analysis of the function f(x) at a particular value of x, where the function has a positive value and a positive but decreasing slope. Based on the given options, we can eliminate the linear function y=13x, as its slope is constant and positive, not decreasing.

Considering the option y=x², at x=3, f(3)=9, which is positive. The slope of the function (represented by the derivative) is 2x, so at x=3, the slope is 2(3)=6, which is also positive. Furthermore, as x increases, the magnitude of the slope also increases, not decreases.

Therefore, neither of these options fully matches the conditions described in the question. The graph of a function is often created by plotting specific x, y data pairs, and optionally, the characteristics of the derivative of the function can be analyzed to understand the nature of the slope at given points.

The graph of the function is shown to y=(12)/(13)(x²-25)²/³-example-1
User Muhammed Moussa
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