Calculus (Urgent Help)

Okay, I need major help! Can someone tell me if these statements are true or false ASAP please. Thank you.

1. If ƒ′(x) < 0 when x < c then ƒ(x) is decreasing when x < c.

True

2. The function ƒ(x) = x^3 – 3x + 2 is increasing on the interval -1 < x < 1.

False

3. If ƒ'(c) < 0 then ƒ(x) is decreasing and the graph of ƒ(x) is concave down when x = c.

True

4.A local extreme point of a polynomial function ƒ(x) can only occur when ƒ′(x) = 0.

True

5. If ƒ′(x) > 0 when x < c and ƒ′(x) < 0 when x > c, then ƒ(x) has a maximum value when x = c.

False

6. If ƒ′(x) has a minimum value at x = c, then the graph of ƒ(x) has a point of inflection at x = c.

False

7. If ƒ′(c) > 0 and ƒ″(c), then ƒ(x) is increasing and the graph is concave up when x = c.

True

8. If ƒ′(c) = 0 then ƒ(x) must have a local extreme point at x = c.

False

9. The graph of ƒ(x) has an inflection point at x = c so ƒ′(x) has a maximum or minimum value at x = c.

True

10. ƒ′(x) is increasing when x < c and decreasing when x > c so the graph of ƒ(x) has an inflection point at x = c.

True

So yeah those are the questions (statements), if you can tell which ones are true / false or correct me on what I said that would be helpful. I put what I thought it was so if its wrong, please correct me! Thanks,

Veronica!!

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  1. 1. T agree - if x is increasing, f(x) is decreasing
    2. F agree - max at x = -sqrt 3, min at x = +sqrt 3
    3. False, disagree, it is decreasing but who says it is concave or convex? It could be a straight line with negative slope.

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  2. 4.A local extreme point of a polynomial function ƒ(x) can only occur when ƒ′(x) = 0.

    True AGREE

    5. If ƒ′(x) > 0 when x < c and ƒ′(x) < 0 when x > c, then ƒ(x) has a maximum value when x = c.

    TRUE I think - DISAGREE looks like /\

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  3. 6. If ƒ′(x) has a minimum value at x = c, then the graph of ƒ(x) has a point of inflection at x = c.

    False
    TRUE - DISAGREE
    an extreme value of f' means f" changes sign which means inflection

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  4. Agree with 7 8 9 10

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  5. oh okay, thanks so much! :) i really appreciate the help, especially since u corrected what i did wrong. thanks!

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  6. I hope you realize by doing this you are helping students taking online calculus cheat on their test, as this is direct content from the test under Unit 6 Activity 9.

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  7. Not only that, but you are wrong on number 6.

    A minimum value of f'(x) at x = c does NOT imply an extreme value, although the reverse is certainly true if the sign changes from - to +.

    f''(x) could be undefined at f'(c) which would make it a critical value of f'(x) since it is in the domain of f'(x). An example would be if f'(x) = x ^ (1/2).

    (0,0) is clearly a minimum value of f'(x), and in fact f(x), but it is not a relative minimum so there would be no inflection point.

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