Find the average value of the function on the given interval.f(x) = x2 e4x; [0, 3] Give your answer in exact form.

A. e12  - 
B. e12  - 
C. e12 
D. e12  - 

Answer: B

Mathematics

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Multiply.x2(-8x2 + 40x + 8)

A. 2x4 + 10x3 + 2x2 B. -2x4 + 20x3 + 8x2 C. 10x4 + 2x2 D. -2x4 + 10x3 + 2x2

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Mathematics

Determine whether the given function satisfies a Laplace equation.f(x, y, z) = cos (7x) sin (7y) e(z)

A. Yes B. No

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Mathematics

Find the coordinates of the vertex of the quadratic function.f(x) = -6x2 - 12x - 3

A. (2, -51) B. (-2, -15) C. (-1, 3) D. (1, -21)

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Mathematics

Use the Intermediate Value Theorem to determine whether the polynomial function has a zero in the given interval.f(x) = 5x4 + 3x3+ 9x - 10; [-2, -1]

A. f(-2) = 28 and f(-1) = -17; yes B. f(-2) = -28 and f(-1) = -17; no C. f(-2) = -28 and f(-1) = 17; yes D. f(-2) = 28 and f(-1) = 17; no

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Mathematics