Answer:
To find the speed, we need to calculate the derivative of the distance function \(d(h)\) with respect to time \(t(h)\). Let me perform that calculation for you:
\[ \frac{d}{dt}(d(h)) = \frac{d}{dh}(d(h)) \times \frac{dh}{dt} \]
Given \(d(h) = 6h^2 - h - 1\) and \(t(h) = 2h - 1\), the derivative is:
\[ \frac{d}{dt}(d(h)) = (12h - 1) \times 2 \]
Simplifying:
\[ \frac{d}{dt}(d(h)) = 24h - 2 \]
Now, we want to express this speed function in terms of \(h\), so we can compare it with the given options:
\[ \frac{d}{dt}(d(h)) = 24h - 2 = 2(12h - 1) \]
Comparing with the options, it matches option:
b. \( (d/t)(h) = 12h^3 + 2h^2 - 2h \)