Decide whether each statement is true or false. This week, for a change of pace,

Question

Decide whether each statement is true or false.

This week, for a change of pace, decide whether each stateament is true or false. Careful! Please provide an easy to read answer sheet for the Group Report. 1. It is impossible for a function to haive both a horizontal asymptote and a vertical asymptote. 2 Adding two functions that are continuous everywhere wil always yield a function that is continuous 17. if afta/d Dthen fix) is a constant is a consequence of the Mean Value Theorem. ? 8 if dng/d., derxyde everywhere, then tlxJ-etx) is constant. 19. For both Rolle's Theorem and the Mean Value Theorem, the function fxi is assumed to be continuous on a dosed interval and differentieble on an open interval. Every continuous function no.1)-? R (where R represents the set of real numbers) has a maimum s. )exists, then ) must have a horizontal asymptote. 4. If tx) is not continuous at x-s, then it cannot be differentiable at x-a. S The property Intry)-In) Inly) halds for xo0 and yso. 6 For a continucus function fixi, a point x-a in the domain of fex) cennot be both a critical point and an 22 1x1/1 can be ottered usnestanara nie. 23 Although Gui taume de hioritel was the fir t to publish his famous rule, it was actually discovered Johann Bemouli. inflection point Isaec Newton and Gotfried Leibriz developed Gifferensial and integralt cakculus at about the seme time, one in England and the other in Germany 24 7. i-0or is undefined, and if c is in the domain of f, then f has an inflection point at x c 8. It jx) evalustes to ofoo at x-s then Jim f(x) can be computed uine topte Rule. 9. If fx) is an arbitrary quadratic function, then it is guaranteed to have a critical point within its 25. Cokculi is Lain for pebbles domain, 10. It fik) ls continuous on la.b] then fxy is kiteratatls on la.b 11 t fto) s continuous on la,al then flx) is difterentiable on tsbl 121rNx) is differentiable oalabl thenfe, is continuousonlabl 13. The derivetive of a constant is a constant 14. The integral of a constant is a conctant. 15. The integral of a polynornial is a polynomial 16. At some time during an automobile trip, that the instantaneous speed is equal to the average meanj speed over the entire trip is a consequence of Rolle's Thecrem, h United States ai e

Explanation / Answer

Answwering first 15 questions:-

1. False. It is possible, for example xy=c.

2. True.

3. True.

4. True.

5. False. The property is not possible for any x and y.

6. True. Critical points refer to first derivatives, while inflection points relate to second derivatives.

7. False. It may be true or may not be.

8. True.

9. true.

10. True.

11. False. Not always true.

12. True.

13. True. It is zero always.

14. False. It is true only for integral of zero.

15. True.

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