GRE Exam Numerical Ability Geometry

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

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GRE Other Question

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) Let f(x, y) = x^2 – 2xy + y^3 for all real x and y. Which of the following is true.
(A) f has all of its relative extrema on the line x y.
(B) f has all of its relative extrema on the parabola x = y^2
(C) f has a relative minimum at (0, 0)
(D) f has an absolute minimum at (2/3, 2/3)
(E) f has an absolute minimum at (1, 1)