The graph of f ′(x) is continuous and increasing with an x-intercept at x = 5. Which of the following statements must be true?

Question

anonymous · Answer

tkhunny · Answer

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Compare the statements.

anonymous · Answer

@IrishBoy123  can you confirm for me?

anonymous · Answer

None of these are true.

anonymous · Answer

@jim_thompson5910 You wanna lend me a hand? God bless.

jim_thompson5910 · Answer

look at @tkhunny 's graph

jim_thompson5910 · Answer

if x is something less than 5, is f ' (x) positive? or negative?

anonymous · Answer

Negative.

irishboy123 · Answer

i agree

jim_thompson5910 · Answer

how about if x is greater than 5? what is the sign of f ' (x) ?

anonymous · Answer

Positive.

anonymous · Answer

Does that mean it's an inflection point?

jim_thompson5910 · Answer

|dw:1446679585637:dw|

anonymous · Answer

Because at that point it changes from positive to negative.

jim_thompson5910 · Answer

|dw:1446679602023:dw|

jim_thompson5910 · Answer

|dw:1446679634672:dw|

jim_thompson5910 · Answer

`f ′(x) is continuous and increasing`

if f ' (x) is always increasing, what do we know about f '' (x) ?

anonymous · Answer

Is also increasing increasing?

anonymous · Answer

always*

jim_thompson5910 · Answer

what is the slope of f ' (x)

I don't care about the actual number. I only care about if it is positive or negative

anonymous · Answer

Positive.

jim_thompson5910 · Answer

it's always positive, so f '' (x), whatever it is, will always be positive

if f '' (x) is positive, then f(x) is concave up