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Given the function f(x) = -3x^2 + 18x + 10, identify the maximum/minimum value of the function.

a) minimum: (0, 10)
b) minimum: (3, 37)
c) maximum: (3, 37)
d) maximum: (0, 10)

User Lilezek
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2 Answers

5 votes

Answer: You would add 18 + 10 then add -3x^2 and you will get your answer.

Step-by-step explanation:

User Malcolm Box
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3 votes

Final answer:

The maximum value of the function f(x) = -3x^2 + 18x + 10 is at the point (3, 37) because this is a downward-opening parabola, and the vertex of the parabola represents the maximum value of the function.

Step-by-step explanation:

To identify the maximum or minimum value of the function f(x) = -3x^2 + 18x + 10, we can first recognize that this is a quadratic function in the form of ax^2 + bx + c, where a = -3, b = 18, and c = 10. The coefficient of x^2 (a) is negative, indicating that the parabola opens downwards, hence the function has a maximum value rather than a minimum.

To find the x-coordinate of the vertex, we use the formula -b/(2a), which gives us -18/(2×(-3)) = 3. Substituting x = 3 back into the function, we get f(3) = -3(3)^2 + 18(3) + 10 = -27 + 54 + 10 = 37. Hence, the maximum value of the function is at the point (3, 37).

User Diego Favero
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