The graph of a function f is given below
Select the graph of f ' from the 4 following options.
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hard to keep them straight. is this an on line course?
your original function, if i recall, is increasing and then decreasing. changes direction at 0. so one thing you know is that your derivative must be positive to the left of 0 and negative after. let me review them and see if that eliminates any
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it eliminate the first one because that parabola is alway positive, aka above the x axis. cross it out
second one is positive and then negative, but it is not correct because it is large far to the left of zero and then gets smaller. but your original function is increasing slowly then increasing rapidly, so your derivative should be a small positive number and then a larger one. cross out #2
what do you mean by it gets smaller after zero?
#3 looks good because where your original function is increasing slowly this one is close to zero but positive. then where your function is increasing more rapidly this one is bigger. then it drops quickly to zero
for #2 i am only looking to the left of the y axis.
your original function is increasing there so your derivative has to be positive.
but your original function is increasing first slowly and then more rapidly
the derivative gives the slope of the tangent lines. if you look at your original function you will see that the slope of the tangent lines is small, that is close to zero, as you start out. then they get steeper so your derivative should get bigger.
#3 you will see that this does just that. it starts out close to zero but then gets larger. this reflects the fact that your original function is increasing slowly and then gets steeper
on the right hand side of the y axis your function is at first decreasing very rapidly, then still deceasing but more slowly. # 3 reflects that as that as soon at is crosses the y axis it drops steeply.