Mr. Lyle made a round trip between two cities that were 450 kilometers apart. On the return trip, he increased his average of ra
1 answer:
Answer:
45 km/h
50 km/h
Step-by-step explanation:
Distance traveled in one way = 450 km
Let x = Velocity when he was going to his destination in km/h
He traveled 5 km/h faster when he returned so his velocity was
It took him 1 hour less when he returned so
So, velocity while going to his destination is 45 km/h
While returning his velocity was 45+5 = 50 km/h.
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Answer:
a) , b)
, c) Concave upward:
. No intervals being concave downward.
Step-by-step explanation:
a) Tangent line is vertical if slope is undefined, whose points are associated with discontinuities of the function. Rational functions have discontinuities associated with the denominator:
By factorizing each component, the function is re-arranged as:
There is no avoidable discontinuities. The only point where tangent line is vertical is .
b) Tangent line is horizontal if slope is equal to zero, whose point is associated to the points that makes function equal to zero. Rational functions have horizontal tangent lines if numerator is equal to zero and denominator is different to zero. Hence, the only point where tangent line is horizontal is .
c) An interval is concave upward if exist an absolute minimum inside, which can be found by the help of the First and Second Derivative Tests.
The only critical point is:
(which coincides with the result of point b)
The value associated with the critical point is:
Which means that critical point is an absolute minimum, and, consequently, the interval that is concave upward is . There is no absolute maximums and, therefore, there is no interval that is concave downward.