Question

Find the slope of c(t)=(t/2,(t^(2)/4) -t) at t=2

Answer 1

Answer on Question #51515 – Math – Differential Geometry

Find the slope of $c(t) = (t/2, (t^2)/4) - t)$ at $t=2$

Solution

$$c(t) = \left(\frac{t}{2}; \frac{t^2}{4} - t\right)$$

The slope is given by the next formula:

$$\text{slope}(t) = \left(\frac{dc_s / dt}{dc_s / dt}\right) = \frac{t / 2 - 1}{1 / 2} = t - 2$$

Then

$$\text{slope}(2) = 2 - 2 = 0$$

Answer: $\text{slope}(2) = 0$.

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