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Find an equation for the slope of the graph of y=6/x³ -7/6 at any point

A. - 6/x²
B.- 18/x⁴
C. 18/x²
D. 6/x⁴

1 Answer

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Final answer:

The slope of the graph of the function y = 6/x³ - 7/6 at any point is the derivative of the function, which is -18/x⁴, aligning with choice B.

Step-by-step explanation:

The student has been asked to find the slope of the tangent to the graph of the function y = 6/x³ - 7/6 at any point.

To find the slope, we need to calculate the derivative of the function concerning x.

This involves using the power rule for differentiation. The derivative of y concerning x is given by:

y' = -18/x⁴

Therefore, the slope of the tangent to the graph at any point is -18/x⁴, which corresponds to choice B.

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