21 July, 07:14
For what value of x will the function f (x) = - 3 (x - 10) (x - 4) have a maximum value? Find the maximum value.
21 July, 08:20
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.
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» For what value of x will the function f (x) = - 3 (x - 10) (x - 4) have a maximum value? Find the maximum value.