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Shay10825
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Hi everyone. I need some help with these 3 problems. Any help would be appreciated.
4. Let f be the function defined by f(x)= ln(2+ sin x) for pi <= x <= 2pi
(a) Find the absolute maximum value and the absolute minimum value of f. Show your analysis that leads to your conclusion.
(b) Find the x-coordinate of each point on the graph of f. Justify your answer.
My work:
f'(x) = (cos x) / (sin x +2)
0= (cos x) / (sin x +2)
0= cos x
x= pi/2
f''(x) = [ (sin x +2)(-sin x ) - (cos x)(cos x) ] / [ (sin x +2)^2 ]
0= (sin x +2)(-sinx) - (cos x)(cos x)
Now here is my problem. How do I solve that??
5. The figure above shows the graph of f', the derivative of a function f. The domain of f is the set of all such that 0<x<2
(a) Write an expression for f'(x) in terms of x
(b) Given that f(1)=, write an expression for f(x) in terms of x
(c) In the xy-plane provided below, sketch the graph of y=f(x)
My Work:
a. for (1,1) and (2,0)
y-0=-1(x-2)
y=-x+2
f'(x) = {x 0<= x <= 1
{-x+2 1<= x <=2
b. 0= .5(1^2) +c
-.5 = c
0= 2(1) -.5(1^2) +c
0=2-.5 +c
-1.5=c
f(x)= {.5x^2 + -.5 0<= x <=1
...{2x - .5x^2 -1.5 1<= x <2
6. Let P(t) represent the number of wolves in a population at time t years, when t>= 0. The population P(t) is increasing as a rate directly proportional to 800-P(y), where the constant of proportionality is k.
(a) If P(0)= 500, find P(t) in terms of t and k
(b) If P(2)=700, find k
(c) Find lim P(t)
...t->x
i have no clue what to do for this one. since it says "rate" it must use related rates but how would you do it??
~Thanks
4. Let f be the function defined by f(x)= ln(2+ sin x) for pi <= x <= 2pi
(a) Find the absolute maximum value and the absolute minimum value of f. Show your analysis that leads to your conclusion.
(b) Find the x-coordinate of each point on the graph of f. Justify your answer.
My work:
f'(x) = (cos x) / (sin x +2)
0= (cos x) / (sin x +2)
0= cos x
x= pi/2
f''(x) = [ (sin x +2)(-sin x ) - (cos x)(cos x) ] / [ (sin x +2)^2 ]
0= (sin x +2)(-sinx) - (cos x)(cos x)
Now here is my problem. How do I solve that??
5. The figure above shows the graph of f', the derivative of a function f. The domain of f is the set of all such that 0<x<2
(a) Write an expression for f'(x) in terms of x
(b) Given that f(1)=, write an expression for f(x) in terms of x
(c) In the xy-plane provided below, sketch the graph of y=f(x)
My Work:
a. for (1,1) and (2,0)
y-0=-1(x-2)
y=-x+2
f'(x) = {x 0<= x <= 1
{-x+2 1<= x <=2
b. 0= .5(1^2) +c
-.5 = c
0= 2(1) -.5(1^2) +c
0=2-.5 +c
-1.5=c
f(x)= {.5x^2 + -.5 0<= x <=1
...{2x - .5x^2 -1.5 1<= x <2
6. Let P(t) represent the number of wolves in a population at time t years, when t>= 0. The population P(t) is increasing as a rate directly proportional to 800-P(y), where the constant of proportionality is k.
(a) If P(0)= 500, find P(t) in terms of t and k
(b) If P(2)=700, find k
(c) Find lim P(t)
...t->x
i have no clue what to do for this one. since it says "rate" it must use related rates but how would you do it??
~Thanks