Reference no: EM13845554
1) ______ Find the intervals on which the functionf(x)=x^(2⁄3) (10-x) is increasing and decreasing. Sketch the graph of y=f(x) and identify any local maxima and minima. Any global extrema should also be identified.
(A) f(x) is decreasing on the interval (-) (-∞,0)∪(4,∞); increasing on (0,4)
(B) f(x) is increasing on the interval (-∞,0)∪(4,∞); decreasing on (0,4)
(C)f(x) is decreasing on the interval (-∞,10)∪(10,∞)
(D) f(x) is increasing on the interval (-∞,0)∪(0,∞)
(E) none of the above
2) ______ Sand falling from a hopper at10π (ft^3)⁄sec forms a conical sand pile whose radius is always equal to its height. How fast is the radius increasing when the radius is 5 ft?
(A) 5 ft⁄sec
(B) 10 ft⁄sec
(C) 2⁄5 ft⁄sec
(D) not enough information
(E) none of the above
(3) _____ Find the values of a and b for which the function g below is differentiable
g(x)={(ax+b x≤-1@ax^3+x+2b x>-1)¦
(A)a=1,b=-1
(B)a=1,b=-1/2
(C)a=1/2,b=-1/2
(D)a=-1/2,b=1
(E) None of the above
(4) ______ Find f^' (x) given
f(x)=1/(1+1/(1+1/x))
(A) 1/(x+2)^2
(B) - 1/(2x+1)^2
(C)-(1+(1+x^(-1) )^(-1) )^(-2)·(-(1+x^(-1) ) )^(-2)
(D) ?-(1+(1+x^(-1) )^(-1) )^(-2)·-x^(-2)
(E) None of the above
(5) _____ Find the derivative of fat x=0 provided it exists. If it does not exist, explain.
f(x)={((1-cos?x)/x x≠0@0 x=0)¦
(A) f^' (0)=0 (B) f^' (0)=1/2 (C) f^' (0)=1 (D) f^' (0) does not exist (E)Noneoftheabove
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: 1) ______ Find the intervals on which the functionf(x)=x^(2⁄3) (10-x) is increasing and decreasing. Sketch the graph of y=f(x) and identify any local maxima and minima. Any global extrema should also be identified.
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