Final answer:
The equation for the slope of the graph of y=6/x³ - 7/6 is found by differentiating the function, resulting in -18/x⁴ (Option B).
Step-by-step explanation:
To find an equation for the slope of the graph of y=6/x³ - 7/6 at any point, we need to differentiate the function with respect to x. The slope of a curve at any point is given by the derivative of the function at that point. The derivative of y=6/x³ - 7/6 with respect to x can be found using the power rule for differentiation.
The derivative of 6/x³ is -18/x⁴ because we bring down the exponent and then subtract one from the exponent (power rule). The derivative of a constant, such as -7/6, is zero. Thus, the equation for the slope of the graph is -18/x⁴, which corresponds to option B.
Here's the step-by-step differentiation:
- d/dx of 6/x³ = 6 * (-3) * x-3-1 = -18/x⁴.
- d/dx of -7/6 = 0, because the derivative of a constant is zero.
- Then combine the two derivatives to get the slope of the graph: -18/x⁴.