Question

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)

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`

Answer 1

II, IV and V

Explanation:

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