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Calculus I - The Shape of a Graph, Part I (Practice Problems) - Free Printable

Educational worksheet: Calculus I - The Shape of a Graph, Part I (Practice Problems). Download and print for classroom or home learning activities.

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Show Answer Key & Explanations Step-by-step solution for: Calculus I - The Shape of a Graph, Part I (Practice Problems)

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Final Answer:
The graph shows a polynomial function with roots at $x = -7$, $x = -2$, and $x = 5$, and it touches the x-axis (without crossing) at $x = -2$, indicating a repeated root (even multiplicity). The end behavior goes down on both ends, so the leading coefficient is negative and the degree is even. A possible equation is:
$$
f(x) = - (x + 7)(x + 2)^2(x - 5)
$$

Parent Tip: Review the logic above to help your child master the concept of derivatives from graphs worksheet.

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