I have two questions
first
Let f be a function that is differentiable on teh open interval (a,b) If f has a relative minimum at (c,f(c)) and a<c<b which of the folowing must be true?
I. f'(c)=0
II. f''(c) must exist
III. If f''(c) exists, then f''(c)>0
I know one is true because f'(c)=0 means c was a critical point and that it had a minimum. I think III is right because f''(c)>0 means it is concave up and that causes a relative minimum or is choice two right? I dont know which one.
second question
The velocity of particle moving along the x-axis is given by a third-degree polynomial P(t). The roots of P(t) are all in the open interval 0<t<a. Which of the following statements must be true?
I. The velocity of the particle will be xero at least once and at most three times for 0,t,a
II. In the interval 0<t<a, the particle moves both left and right.
III. The total distance traveled by the particle from t=0 to t=a is given by ? P(t)dt where lower limit is 0 and upper limit is a
a. I only
b. II only
c. III only
d. I and II only
E. I, II, III
I just dont get this one at ALL. please helpp
first
Let f be a function that is differentiable on teh open interval (a,b) If f has a relative minimum at (c,f(c)) and a<c<b which of the folowing must be true?
I. f'(c)=0
II. f''(c) must exist
III. If f''(c) exists, then f''(c)>0
I know one is true because f'(c)=0 means c was a critical point and that it had a minimum. I think III is right because f''(c)>0 means it is concave up and that causes a relative minimum or is choice two right? I dont know which one.
second question
The velocity of particle moving along the x-axis is given by a third-degree polynomial P(t). The roots of P(t) are all in the open interval 0<t<a. Which of the following statements must be true?
I. The velocity of the particle will be xero at least once and at most three times for 0,t,a
II. In the interval 0<t<a, the particle moves both left and right.
III. The total distance traveled by the particle from t=0 to t=a is given by ? P(t)dt where lower limit is 0 and upper limit is a
a. I only
b. II only
c. III only
d. I and II only
E. I, II, III
I just dont get this one at ALL. please helpp
