The stopping distance d meters of a car is inversely proportional to the square of its speed s km/h when the brakes are applied. A car travelling at 50 km/h requires a stopping distance of 20 metres. If the stopping distance is 500 metres, what is the speed of the car when the brakes are applied?

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step-by-step explanation:

1 number

if we use a graphing calculator, there is only one such number that satisfies the conclusion of the mean value theorem, that is, a number such that

where the right-hand side is the average rate of change of f on the interval [0.5,0.75], which is the slope of the secant line.

in the attached graph, the black line is the secant line which has its slope as the average rate of change of f on [0.5,0.75], while the orange line is the only tangent line to the graph of f in the interval that satisfies the mvt conclusion.

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