Explain why the curve y = I7x 3 + 12x - 9 does not have a tangent line with a sl

Question

Explain why the curve y = I7x 3 + 12x - 9 does not have a tangent line with a slope less than 12. Choose the best explanation. Since the derivative of y has a constant term 12. The slope of the tangent line will always equal this constant term and is therefore never less than 12. Since setting the derivative of y equal to zero, then solving for x results in a value greater than 12, the slope must be greater than 12. Since the derivative of y is the function for the slope of the tangent line. Since the constant term in y is less than 12, the slope will never be less than 12. Since the derivative of y is a squared term and a constant term, 12, then regardless of what x-value is substituted, the slope will never be less than that constant term.

Explanation / Answer

derivative = 51x^2 + 12 >= 12 always therefore, D is the answer.

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