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.