Demetri is studying a new function g and has concluded that g is decreasing at #x = 5#. Which of the following can Demetri now conclude? [Choose all that apply] (Choices below)

Question

I say that it is II, V, and either III or IV? Can you just double-check?

I. The slope of the tangent line to g at #x = 5# is positive

II. The slope of the tangent line to g at #x = 5# is negative

III. The rate of change of #g# at #x = 5# is positive

IV. The rate of change of #g# at #x = 5# is negative

V. #g'(5) < 0#

VI. #g'(5) > 0#

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Answer 1 · 2017-03-04T22:14:33

II, IV and V

The definition of an increasing or decreasing function is that

# { (y' < 0),(y' > 0) :} => {: (y " is decreasing"), (y " is increasing") :} #

So if #g(5)# is decreasing #=> g'(5) < 0 #

#g'(x)# also represents the rate of change and the gradient of the tangent.

Hence the correct solutions are:

II, IV and V