Respuesta :
Hello!
To find the maximum value of the function f(x) = -3(x - 10)(x - 4), the easiest way is to find the vertex using the formula: x = -b/2a.
Firstly, we need to simplify f(x).
f(x) = -3(x - 10)(x - 4)
f(x) = -3(x² - 14x + 40)
f(x) = -3x² + 42x + -120
Since the equation f(x) is now simplified to standard form, we can find the vertex.
a = -3, b = 42, and c = -120
x = -(42)/2(-3) = -42/-6 = 7
Then, we substitute 7 into the the function f(x) = -3(x - 10)(x - 4), or
f(x) = -3x² + 42x + -120, to find the y-value of the vertex.
f(x) = -3(7 - 10)(7 - 4)
f(x) = -3(-3)(4)
f(x) = 27
The vertex of f(x) is (7, 27).
Therefore, the maximum x-value for the function f(x) is 7.
Maximum point occurs at the line of symmetry
Step 1: Find the x-intercept. [ x- intercept = when f(x) = 0 ]
f(x) = -3(x - 10)(x - 4)
-3(x - 10)(x - 4) = 0
x - 10 = 0 or x - 4 = 0
x = 10 or x = 4
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Step 2 : Find the line of symmetry [ Midpoint of x ]
midpoint of x = (10 + 4) ÷ 2 = 7
Line of symmetry : x = 7
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Answer: Maximum value occurs when x = 7
