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Answer:
Step-by-step explanation:
Let t represents the time in hours,
We know that,
Since, the speed of truck = 30 miles per hour,
So, the distance covered by the truck in t hours = 30t miles,
Similarly,
Speed of car = 60 miles per hour,
So, the distance covered by car in t hours = 60t miles,
∵ Truck is 300 miles east of the car initially,
Thus, the distance of the truck from the starting point = 30t + 300,
While the distance of the car from the starting point = 60 t,
Now, these two vehicles are going in the directions which are at right angled ( car is going north and truck is going west )
Using the Pythagoras theorem,
Distance between them after t hours,
Which is the required function.
We want to get the difference quotient for the given function, we will get see that the difference quotient is equal to:
f'(x) = 2x + 5
<h3>The difference quotient:</h3>
For a given function f(x), we define the difference quotient as:
In this case, we have:
f(x) = x^2 + 5x + 6
Replacing that in the difference quotient we get:
Now we can cancel the factor h to get:
So the difference quotient is equal to 2x + 5.
If you want to learn more about difference quotients, you can read: