GRE Exam Programming Functions

Let f and g be twice-differentiable real-valued functions defined on R. If f’(x) > g’(x) for all x > 0, which of the following inequalities must be true for x > 0?
(A) f(x) > g(x)
(B) f”(x) > g”(x)
(C)f(x) – f(0) > g(x) – g(0)
(D) f’(x) – f’(0) > g’(x) – g’(0)
(E) f”(x) – f”(0) > g”(x) – g”(0)

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GRE Other Question

Let V be the real vector space of all real 2*3 matrices, and let W be the real vector space of all real 4*1 column vectors. If T is a linear transformation from V onto W, what is the dimension of the subspace.
(A) 2
(B) 3
(C)4
(D) 5
(E) 6
For what value of b is the line y = 10 x tangent to the curve y = e^(bx) at some point in the xy-plance?
(A) 10/e
(B) 10
(C) 10 e
(D) e^10
(E) e