SOLUTION: Let f(x) = 2x^2 &#8722; 9x. Find all extreme values (if any) of f on the interval [0, 9]. Determine at which numbers in the interval these values occur. NOTE: If there is no max

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Question 995804: Let f(x) = 2x^2 − 9x.
Find all extreme values (if any) of f on the interval [0, 9]. Determine at which numbers in the interval these values occur. NOTE: If there is no maximum value (or minimum value), then enter DNE in the corresponding blanks.
Maximum Value:
Minimum Value:
Found 2 solutions by MathLover1, stanbon:
Answer by MathLover1(20850) (Show Source):
You can put this solution on YOUR website!
Definition: Maximum and Minimum of a function
1. A function has a maximum at if for all in the domain of .
2. A function has a minimum at if for all in the domain of .
The values of the function for these x-values are called extreme values or extrema.

here you have a parabola
the least or greatest value of the parabola could be found at the vertex of the parabola (on the axis of symmetry )
=> =>minimum is at =>=>=>
or, find it using derivative:
'
=>=>

Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website!
Let f(x) = 2x^2 − 9x
Then f'(x) = 4x-9
And f"(x) = 4
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Find all extreme values (if any) of f on the interval [0, 9]. Determine at which numbers in the interval these values occur. NOTE: If there is no maximum value (or minimum value), then enter DNE in the corresponding blanks.
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Solve 4x-9 = 0
x = 9/4
Since f"(9/4) = 4 > 0,
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Maximum Value: DNE
Minimum Value: f(9/4) occurs at x = 9/4
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Cheers,
Stan H.
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SOLUTION: Let f(x) = 2x^2 &#8722; 9x. Find all extreme values (if any) of f on the interval [0, 9]. Determine at which numbers in the interval these values occur. NOTE: If there is no max

SOLUTION: Let f(x) = 2x^2 − 9x. Find all extreme values (if any) of f on the interval [0, 9]. Determine at which numbers in the interval these values occur. NOTE: If there is no max