Get The Figure Above Is The Graph Of A Function Of X Which Models The Height Of A Skateboard Ramp

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1. Click the ‘Get Form’ button to obtain the form and open it in an online editor.
2. Familiarize yourself with requirement (i) which states that at x = 0, the value of the function is 0, and the slope of the graph is also 0. Make sure to incorporate these values in your modeling.
3. Refer to requirement (ii) which indicates that at x = 4, the function value must equal 1 and the slope at this point must equal 1. Experiment with different functions to meet this requirement.
4. In part (a), document your findings that a quadratic function of the form f(x) = ax^2 does not meet the second requirement by calculating the derivative and output values.
5. In part (b), explore cubic functions like g(x) = cx^3 - (1/16)x^2 and identify the coefficient c that allows it to meet requirement (ii). Show your calculation steps.
6. In part (c), illustrate your work to demonstrate that function g does not satisfy requirement (iii) by analyzing its output across the specified interval.
7. For part (d), identify the values of k and n for the power function h(x) = kx^n that meet all three requirements. Present your calculations clearly.
8. Once all sections are completed, you can save your changes, download your document, print it, or share it directly from the online editor.

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