If the graph of f''(x) is continuous and has a relative maximum at x=c, which of the following must be true?

A.The graph of f has an x-intercept at x=c
B. The graph of f has an inflection point at x=c
C.The graph of f has a relative minimum at x=c
D. None of the above are necessarily true.

Question

If the graph of f''(x) is continuous and has a relative maximum at x=c, which of the following must be true?

A.The graph of f has an x-intercept at x=c
B. The graph of f has an inflection point at x=c
C.The graph of f has a relative minimum at x=c
D. None of the above are necessarily true.

helpmeeplz · Answer

@AloneS

alones · Answer

Okay so let's look at each choice

helpmeeplz · Answer

ok

alones · Answer

In A the point on a curve where a moving point on the curve must start to move backward.

alones · Answer

OKay let's looks at b

alones · Answer

So b has The graph of f has an inflection point at x=c. It states that if f(x) is defined and continuous on the interval [a,b] and differentiable on (a,b). So I don’t think that would be b neither

helpmeeplz · Answer

Ok, I see that.

helpmeeplz · Answer

Will it all just depend on the particular equation, making the answer be D?

alones · Answer

“Sketch the graph of y = −x3 − 2x2 + x + 2. [Hint: Call the function −f(x), then factor f(x) by grouping.]”so this how would we graph the graph f’(x), but choices don’t show it, so I don’t think neither C would work

alones · Answer

Btw is it a multiple choice for you?

helpmeeplz · Answer

yes. those are the four choices

helpmeeplz · Answer

So, it would be D?

alones · Answer

I believe that is true.

helpmeeplz · Answer

Thanks!