1. If f(x) = 3^x, what is f \'(0)? a. 3 b. 3e c. 3x ln(3) d. ln(3) e. None of th
ID: 3285306 • Letter: 1
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1. If f(x) = 3^x, what is f '(0)? a. 3 b. 3e c. 3x ln(3) d. ln(3) e. None of the above 2. If f(x) = xe^x, find f ''(0). a. 0 b. 1 c. 2 d. 3 e. None of the above 3. If f(x) = tan(x), find f ''( 4 ). a. 2 ROOT 3 b. 2ROOT2 c. -2 d. 4 e. None of the above 4. If f(x) is invertible with inverse g(y), then g '(y) is a. 1/f(g(y)) b. 1/f '(g(y)) c. 1/f(x) d. undefined e. None of the above 5. If f ''(x) > 0 for all x in an interval, then a. f(x) is increasing on the interval b. f(x) is decreasing on the interval c. f(x) is concave upwards on the interval d. f(x) is concave downwards on the interval e. None of the above 6. If La(x) is the linear approximation to f(x), then a. the graph of La(x) is the tangent line to f(x) through (a, f(a)) b. La(a) = f(a) c. La'(a) = f '(a) d. All of the above e. None of the above 7. Find the interval on which the graph of f(x) = ln(x^2 + 1) is concave upward. a. (-1,1) b. (-1,2) c. (-2,1) d. (?1,1) e. None of the above 8. Using logarithmic differentiation, find the derivative of f(x) = x^x. a. x^x?1 b. x^x c. x^x(ln(x) + 1) d. e^x ln(x) e. None of the above 9. Find the linear approximation L(x) of the function f(x) = tan(x) at a = 0. a. L(x) = x b. L(x) = 1 + x c. L(x) = sec^2(x) d. L(x) = 1 + sec^2(x) e. None of the above 10. Find the linear approximation L(x) of the function f(x) = e^x at a = 0. a. L(x) = x b. L(x) = 1 + x c. L(x) = 1 + x + x^2 d. L(x) = 1 + x^2 e. None of the above 11. Find the linear approximation L(x) of the function f(x) = ROOT x + 3 at a = 1 and use it to approximate the number ROOT 4.05. a. 2.0123 b. 2.0124 c. 2.0125 d. 2.0126 e. None of the above 12. Find the linear approximation L(x) of the function f(x) = 3 ROOT 1 + x at a = 0 and use it to approximate the number 3 ROOT 0.95. a. 0.9830 b. 0.9831 c. 0.9832 d. 0.9833 e. None of the above 13. Use NewtonExplanation / Answer
1=C 2=A 3=B 4=C 5=A 6=A 7=D 8=A 9=A 10=C 11=C 12=C 13=A 14=B
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