A bicyclist is riding on a path modeled by the function f(x) = 0.03(10x − x2), where x and f(x) are measured in miles. Find the rate of change of elevation at x = 1.

Step-by-step explanation:

Given

Path is changing according to the function

Rate of change of the elevation is given by the derivative of the function

At

∠acb = 8°

step-by-step explanation:

∠xba lies on the circle and is half the measure of the intercepted arc ax

hence

measure of arc ax = 2 × 42° = 84°

∠acb is outside the circle and is

∠acb = (arcab - arcax ), hence

∠acb = 0.5 (100 - 84) = 0.5 × 16° = 8°