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BilloRani2012
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Homework Statement
Check for minimum:
When you've got your x value and sub it back into the f'(x) equation, should you get zero if it's a minimum?
BilloRani2012 said:Homework Statement
Check for minimum:
When you've got your x value and sub it back into the f'(x) equation, should you get zero if it's a minimum?
Homework Equations
The Attempt at a Solution
BilloRani2012 said:okay thanks :)
could you please help me with this question:
Any two vectors that are not parallel define a plane. So p = i + j - k and q = 2i + j define a plane. For what values of x is the vector r = xi + j + k in this plane?
ITS DUE TMRW!
Thanks :)
What is the minimum of f(x) = x on the interval 1 <= x <= 2? Is the derivative of f equal to zero there?Disconnected said:Absolutely!
If you got some value other then zero for the rate of change, then the value just to one side of that point would have a lower value, right? So it wouldn't be a minimum!
Aren't you going backwards here? Presumably you got an equation by setting f'(x) to zero, and then you solved for x in the equation f'(x) = 0. The solutions to this equation are possible candidates for being minima or maxima or neither.BilloRani2012 said:Homework Statement
Check for minimum:
When you've got your x value and sub it back into the f'(x) equation, should you get zero if it's a minimum?
Ray Vickson said:What is the minimum of f(x) = x on the interval 1 <= x <= 2? Is the derivative of f equal to zero there?
RGV
If you goal is finding global minima or maxima, you want to look atDisconnected said:Of course. Very good point that I missed completely. I was thinking global minimums.
First of all: I don't see what this has to do with the Original Post in this thread -- the question about the minimum.BilloRani2012 said:Okay so the question was:
Any two vectors that are not parallel define a plane. So p = i + j - k and q = 2i + j define a plane. For what values of x is the vector r = xi + j + k in this plane?
My tutor said to find the the dot product of p and q. But we can't because p has 3 values and q just has 2 values??
Mark44 said:If you goal is finding global minima or maxima, you want to look at
1) values of x for which f'(x) = 0.
2) values of x in the domain of f for which f' is undefined.
3) endpoints of an interval on which the function is defined.
The minimum of a function is the lowest value that the function takes on within a given interval. It is also referred to as the "global minimum" or the "absolute minimum."
To find the minimum of a function, you can use the process of optimization. This involves taking the derivative of the function, setting it equal to zero, and solving for the critical points. You can then plug these critical points back into the original function to determine which one gives the minimum value.
Yes, a function can have multiple minimum values. These are known as "local minima" and occur at points where the function has a slope of zero, but there are other points with lower values nearby. The global minimum is the lowest value overall, while local minima are the lowest values in their respective regions.
Finding a minimum refers to the process of determining the exact value of the minimum point of a function. This involves finding critical points and evaluating them in the original function. Finding a minimum value refers to simply identifying the lowest value that the function takes on within a given interval, without necessarily knowing the exact location of the minimum point.
Yes, calculus can be used to find the minimum of any function that is continuous and differentiable within the given interval. However, the process may become more complex for functions with multiple variables or more complicated expressions.