Question

Am I answering this calculus word problem correctly?

A differentiable function, f(x), has one critical number at x = 4. Classify the relative extrema of g(x) at the critical number if g ‘(3.5) = 3 and g ‘(7)= -13.2. Justify your answer in a complete sentence.

I think its asking for the points that are closest to g'(4). So I put.

g'(3.5)=3 g'(7)=-13.2

Slope:

(-13.2-3)/(7-3.5)=-16.2/3.5

So the points that are closest to g'(4) = -16.2/3.5

Am I reading this question correctly?

Answer 1

im on critical nums in my calc class and dont get it

Answer 2

:)

Answer 3

@surjithayer

Answer 4

I assume
**A differentiable function, f(x), has one critical number at x = 4. Classify the relative extrema of g(x) at the critical number if g ‘(3.5) = 3***
means g(x) not f(x)

when they say g(x) has a critical number at x=4, they mean
g'(4) = 0
You are at a maximum, a minimum or an inflection point.

they want to know which of the 3 types it is.

Answer 5

They tell you
g ‘(3.5) = 3 and g ‘(7)= -13.2

that means at x=3.5, the curve has a slope of +3
and at x=7 the curve has a slope of -13.2



we don't know what value g(3.5) has, but we know g(x) is going up. If "flattens out" at g(4), by x=7, g(7) is going down fast.

Based on that, I would say g(4) is a maximum