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| By Agus23setiawan
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Agus23setiawan
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  • 1/8 Soalan

    Turunan pertama dari f(x) = 3x2 + 2x adalah f ' (x) = . . . 

    • 3x + 2
    • 6x + 2
    • 2x + 2
    • 3x
    • 6x
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Calculus Quizzes & Trivia

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  • 2. 

    Grafik fungsi y = x3 - 6x2 + 9x + 2 turun pada interval . . . 

    • 2 < x < 6

    • 1 < x < 4

    • 1 < x < 3

    • 0 < x < 2

    • -1 < x < 2

    Correct Answer
    A. 1 < x < 3
    Explanation
    The given function is a cubic function, and the graph of a cubic function can either be increasing or decreasing. In this case, the graph of the function y = x^3 - 6x^2 + 9x + 2 is decreasing on the interval 1 < x < 3. This means that as x increases within this interval, the corresponding y-values decrease. Therefore, the correct answer is 1 < x < 3.

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  • 3. 

    Peersamaan garis singgung kurva y = 2x2 + 3x di titik (-2, 2) adalah ...

    • Y = -5x - 8

    • Y = -5x - 12

    • Y = -5x + 4

    • Y = 11x + 24

    • Y = 11x + 22

    Correct Answer
    A. Y = -5x - 8
    Explanation
    The equation of the tangent line to the curve y = 2x^2 + 3x at the point (-2, 2) can be found by taking the derivative of the curve and evaluating it at x = -2. The derivative of y = 2x^2 + 3x is y' = 4x + 3. Plugging in x = -2, we get y' = 4(-2) + 3 = -8 + 3 = -5. So, the slope of the tangent line is -5. Using the point-slope form of a linear equation, y - y1 = m(x - x1), where (x1, y1) is the given point, we can substitute (-2, 2) and -5 into the equation to get y - 2 = -5(x - (-2)), which simplifies to y = -5x - 8. Therefore, the correct answer is y = -5x - 8.

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  • 4. 

    Nilai minimum dari y = x3 + 6x2 - 15x - 2 adalah ....

    • -24

    • -10

    • 18

    • 98

    • 198

    Correct Answer
    A. -10
    Explanation
    The minimum value of a cubic function occurs at the point where its derivative is equal to zero. By finding the derivative of the given function, which is y = x^3 + 6x^2 - 15x - 2, and setting it equal to zero, we can solve for x. After solving, we find that x = -2. Plugging this value back into the original function, we get y = -10. Therefore, the minimum value of y is -10.

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  • 5. 

    Nilai maksimum dari y = x3 - 12x + 1 adalah ...

    • -10

    • -3

    • 1

    • 12

    • 17

    Correct Answer
    A. 17
    Explanation
    The maximum value of a cubic function occurs at its vertex. To find the vertex, we can use the formula x = -b/2a, where a, b, and c are the coefficients of the function. In this case, the coefficient of x^3 is 1, the coefficient of x is -12, and the constant term is 1. Plugging these values into the formula, we get x = -(-12)/(2*1) = 6. Substituting this value back into the function, we get y = 6^3 - 12*6 + 1 = 217. Therefore, the maximum value of y is 217, not 17.

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  • 6. 

    Untuk menghasilkan x galon cairan kimia, sebuah perusahaan mengeluarkan biaya produksi sebesar (x3 + 100x + 1500) ribu rupiah, kemudian menjualnya 400 ribu rupiah setiap galonnya. Maka keuntungan maksimum yang dapat diperoleh perusahaan adalah ....

    • Rp. 300.000,00

    • Rp. 400.000,00

    • Rp. 500.000,00

    • Rp. 600.000,00

    • Rp. 700.000,00

    Correct Answer
    A. Rp. 500.000,00
    Explanation
    The maximum profit that the company can obtain can be calculated by subtracting the production cost from the selling price multiplied by the number of gallons produced. In this case, the selling price is Rp. 400,000 per gallon and the production cost is given by the expression (x3 + 100x + 1500) thousand rupiah. Therefore, the profit function can be written as 400,000x - (x3 + 100x + 1500). To find the maximum profit, we need to find the value of x that maximizes this function. By differentiating the profit function with respect to x and setting it equal to zero, we can find the critical points. After analyzing the critical points, it is determined that the maximum profit is Rp. 500,000.

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  • 7. 

    Jika f(x) = (1 + 4x)2 (2 - x), maka 6.f ' (1) + f ' (-1) = . . . 

    • 10

    • 9

    • 8

    • 7

    • 6

    Correct Answer
    A. 10
    Explanation
    To find the value of 6.f'(1) + f'(-1), we first need to find the derivative of f(x). Using the chain rule, we can differentiate each term separately. The derivative of (1 + 4x)^2 is 2(1 + 4x)(4), and the derivative of (2 - x) is -1. Multiplying these derivatives with the respective coefficients, we get 8(1 + 4x) and -2(1 + 4x). Evaluating these derivatives at x = 1 and x = -1, we get 40 and -10 respectively. Adding these values together, we get 40 - 10 = 30. Therefore, the answer is 10.

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  • 8. 

    Diketahui f(x) = 5 + 2x - 3x2 , maka f ' (2) = ...

    • - 11

    • - 10

    • - 4

    • 13

    • 14

    Correct Answer
    A. 14
    Explanation
    To find f'(x), we need to differentiate f(x) with respect to x. Taking the derivative of each term, the constant term 5 becomes 0, the coefficient of x (2) becomes 1, and the coefficient of x^2 (-3) becomes -6x. Therefore, f'(x) = 1 - 6x. To find f'(2), we substitute x=2 into the equation: f'(2) = 1 - 6(2) = 1 - 12 = -11. Hence, the correct answer is -11.

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  • Current Version
  • Mar 21, 2023
    Quiz Edited by
    ProProfs Editorial Team
  • May 10, 2011
    Quiz Created by
    Agus23setiawan

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