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
Algebra.Com
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
----------------------
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.
----
Solve 4x-9 = 0
x = 9/4
Since f"(9/4) = 4 > 0,
-------
Maximum Value: DNE
Minimum Value: f(9/4) occurs at x = 9/4
==========
Cheers,
Stan H.
-----------
--------------
RELATED QUESTIONS
Let f (x) = e^x - e^4x
Find all extreme values (if any) of f on the interval [0, 1].... (answered by jim_thompson5910)
Let f (x) = x^2 − 5/x
Find all extreme values (if any) of f on the interval [1, (answered by jim_thompson5910)
Let f (x) = 10x^(8/3)
Find all extreme values (if any) of f on the interval [-8, 8].... (answered by jim_thompson5910)
Let f(x) = 2x^2 - 9x Find all extreme values (if any) of f on the interval [0, 9]
So... (answered by Alan3354,solver91311)
Determine the location and value of the absolute extreme values of f on the given... (answered by greenestamps)
f(x) = x^3 − 2x^2 − 4x + 8 / x − 2
Find any hole(s) in the graph of f.
(answered by greenestamps)
Determine the location and value of the absolute extreme values of f on the given... (answered by Edwin McCravy)
Determine the location and value of the absolute extreme values of f on the given... (answered by Boreal)
1)The equation defines a one-to-one function f. Determine f -1 and verify that f f -1... (answered by solver91311)