After Julia had driven for half an hour, she was 155 miles from Denver. After driving 2 hours, she was 260 miles from Denver. Assume that Julia drove at a constant speed. Let f be a function that gives Julia's distance in miles from Denver after having driven for t hours.a. Determine a rule for the function f.b. Interpret f'(500). Calculate f'(500).c. Determine a rule for f'.

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After Julia had driven for half an hour, she was 155 miles from Denver. After driving 2 hours, she was 260 miles from Denver. Assume that Julia drove at a constant speed. Let f be a function that gives Julia&#039;s distance in miles from Denver after having driven for t hours.a. Determine a rule for the function f.b. Interpret f&#039;(500). Calculate f&#039;(500).c. Determine a rule for f&#039;.

Lillianna Mendoza · Accepted Answer

Step 1Since Julia drove at constant speeda) Time and distance follow a linear relation.given at time   t  =  1      /    2 distance   f  =  155 miles and at   t  =  2  h  x     f  =  260  milesi.e. two points on line are   (      1    2    ,  155  ) and (2,260)By two point form, equation of line is  (  f  −  155  )  =            260      −      155              2      −      1              /            2        (  t  −      1    2    )  ⇒  f  −  155  =            105      ×      2        3    (            2      t      −      1        2    )  ⇒  f  −  155  =  35  (  2  t  −  1  )  ⇒  f  =  70  t  +  120  (  1  )Step 2c)       f    ′    =  70 (By differentiating (1))  ⇒      f    ′    (  t  )  =  70  ∀  tStep 3  ⇒  b  )      f    ′    (  500  )  =  70 which is constant speed i.e. 70 miles/hr of Julia

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