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e Find the interval in which f (x) = xe^{9x} is concave upward. e

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e Find the interval in which f(x) = 8x(ln 9x) is concave upward. e

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e What is the interval in which f(x) = (ln(4x))(x) is concave upward ? e

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e What is the interval in which f (x) = 2x^{3} + 18x^{2} + 6x + 30 is concave downward? e

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e Find the interval in which f (x) = 2x  12x is concave downward. e

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e Find the interval in which f (x) = e^{ 7x} is concave downward. e

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e Find the largest interval in which f (x) = 30x^{4} + 6x^{2} + 41 is concave upward. e

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e For the function f (x) = 3ax^{2} + 2bx + 33 where a ≠ 0, which of the following is true? e

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e What is the interval in which f(x) = x  3x  2 is concave downward ? e

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e What is the interval in which f (x) = sin^{2} 6x is concave upward? e

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e What is the interval in which f (x) = tan 4x is concave upward? e

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e What is the interval in which f (x) = e^{7x}  e^{ 7 x} is concave downward? e

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e What is the interval in which f (x) = e^{4x} sin 4x is concave downward? e

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e Find the interval in which f(x) = x22 + ln 5x is concave downward. e

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e Find the interval in which f(x) = 7x ^{2} ln 6x is concave downward. e

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e Find the interval in which f(x) = sin 18x is concave upward. e

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e Find the interval in which f (x) = (ln 7x) ^{2} is concave downward. e

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e What is the interval in which f(x) = x(ln 9x)^{2} is concave downward? e

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e Find the point of inflection of f(x) = x^{3}  12x^{2} + 195. e

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e Determine the point of inflection of the graph of f(x) = 11x e^{17x}. e

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e Find the minimum possible perimeter of a rectangle of area 900 m^{2}. e

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e The sum of two positive numbers is 80. Find the smallest possible value of the sum of their squares. e

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e The sum of two positive numbers is 4. Find the minimum possible value of the sum of the cubes of these numbers. e

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e What is the maximum possible area of a rectangle of perimeter 12 m? e

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e x, y are two positive numbers whose sum is 7. What is the possible greatest value of x^{2} y? e

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e Find the minimum possible perimeter of a rectangle of area 1600 m^{2}. e

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e Find the interval in which f(x) = 5x(ln 6x) is concave upward. e

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e What is the interval in which f(x) = (ln(7x))(x) is concave upward ? e

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e What is the interval in which f (x) = 3x^{3} + 45x^{2} + 12x + 38 is concave downward? e

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e Find the interval in which f (x) = 8x  22x is concave downward. e

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e Find the interval in which f (x) = e^{ 3x} is concave downward. e

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e Find the largest interval in which f (x) = 4x^{4} + 2x^{2} + 28 is concave upward. e

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e What is the interval in which f(x) = x  8x  7 is concave downward ? e

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e What is the interval in which f (x) = sin^{2} 4x is concave upward? e

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e For the function f (x) = 8ax^{2} + 5bx + 31 where a ≠ 0, which of the following is true? e

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e What is the interval in which f (x) = tan 5x is concave upward? e

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e What is the interval in which f (x) = e^{6x}  e^{ 6 x} is concave downward? e

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e What is the interval in which f (x) = e^{7x} sin 7x is concave downward? e

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e Find the interval in which f(x) = x22 + ln 8x is concave downward. e

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e Find the interval in which f(x) = 5x ^{2} ln 4x is concave downward. e

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e Find the interval in which f(x) = sin 4x is concave upward. e

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e Find the interval in which f (x) = (ln 3x) ^{2} is concave downward. e

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e What is the interval in which f(x) = x(ln 5x)^{2} is concave downward? e

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e Find the interval in which f (x) = xe^{5x} is concave upward. e

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e Find the point of inflection of f(x) = x^{3}  6x^{2} + 28. e

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e Determine the point of inflection of the graph of f(x) = 7x e^{13x}. e

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e If f(x) = ax^{2} + bx + c, a ≠ 0, then which of the following is correct? e

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e For a real function y = f(x), which of the following holds true? e

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e What is the maximum possible area of a rectangle of perimeter 16 m? e

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e The sum of two positive numbers is 40. Find the smallest possible value of the sum of their squares. e

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e The sum of two positive numbers is 14. Find the minimum possible value of the sum of the cubes of these numbers. e

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e x, y are two positive numbers whose sum is 10. What is the possible greatest value of x^{2} y? e

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