Growth Rate Calculus Question?
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An analyst has predicted that the growth rate, as percent, for a specific mutal fund can be modelled by the equation
r = 0.5x^3/2 - 6x^2/3 +10.1 , where x is the number of months and x E (0,24). Determine the best and worst times to invest this mutual fund.
Growth Rate Calculus Question?best, january, worst, march
Growth Rate Calculus Question?Since x is in (0, 24), are looking at a period of two years?
Plug in 1, 2, ..., 23 and see which rate is highest.
Growth Rate Calculus Question?First we check the critical value for x, that is the value of x which makes r' (x) = 0 or r'(x) not exist.
Since r'(x) = 0.75x^1/2 - 4x^(-1/3), then r'(x) = 0 if x = 7.454156, and r'(x) will not exist if x =0.
You can check that r''(x) is positive for x = 7.454156, so that r(x) will be minimum for that value.
Since x must be an integer, let we check :
r(0) = 10.1
r(7) = -2.5957
r(8) = -2.5863.
So the best times is when x = 0 and the worst times is when x =7.
Growth Rate Calculus Question?Shane I do not understand this commercial stuff, but look I suggest below.
So r鈥?0.75*x^0.5 鈥?4*x^(-1/3)=0; 0.75x^(5/6) 鈥?4 =0; x=(16/3)^(6/5)=7.454;
Now r(0)=10.1; r(3.15)=0; r(7.454)=-2.62; r(12.58)=0; r(24)=18.97; thus the worst is current July, the best will be in 2 years.
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