%3Cp%3E%3Cspan%20class%3D%22qa-interaction-thread-content%22%3EOpie%20Timization

Question

%3Cp%3E%3Cspan%20class%3D%22qa-interaction-thread-content%22%3EOpie%20Timization%20is%0Aslowing%20down%20as%20he%20approaches%20a%20stop%20light.%20As%20he%20reaches%20the%20stop%0Alight%2C%20he%20has%20slowed%20to%20a%20speed%20of%204%20ft%2Fsec%20and%20the%20light%20turns%0Agreen%20and%20Opie%20begins%20to%20accelerate%20at%20a%3Cbr%20%2F%3E%0Arate%20of%2027%20ft%2Fsec%20for%20the%20first%20eleven%20seconds%20after%20the%20light%0Aturns%20green.Based%20on%20these%20facts%2C%20Opie's%20position%20function%20can%20be%0Ashown%20to%20be%20s(t)%3D%2013.5t%5E2%2B4t%20on%20the%20t%20interval%20%5B0%2C11%5D.%20Use%20the%20MEAN%0AVALUE%3Cbr%20%2F%3E%0ATHEOREM%20to%20prove%20whether%20Opie%20should%20get%20a%20speeding%20ticket%20or%20not.%0AAssume%20a%2035%20mph%20(51.3%20ft%2Fsec)%20speed%20limit.%20NOTE%3A%20You%20must%0Aspecifically%20apply%20the%20THEOREM%20(and%20check%20the%20conditions)%20and%20make%0Athe%20appropriate%20conclusion%20as%20stated%20in%20the%20theorem.%3C%2Fspan%3E%3C%2Fp%3E%0A

Explanation / Answer

mean value theorem

        f'(c ) = f(b) - f(a)/(b-a)

for some c between a and b

               f'(c ) = 1677.5/11 =152.5

so for some time between   0 and 11 sec    spped of the car will be greater than 51.3 ft/sec

hence he will get a ticket

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