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anonymous
 5 years ago
the curve y=f(x) has a minimum point at (3,5)
state the coordinates of the corresponding minimum point on the graph of: y=3f(x) and y=f(2x)
how do i find the coordinates?
and what would the f(x) graph look like??
anonymous
 5 years ago
the curve y=f(x) has a minimum point at (3,5) state the coordinates of the corresponding minimum point on the graph of: y=3f(x) and y=f(2x) how do i find the coordinates? and what would the f(x) graph look like??

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anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0You don't need to know how the graph looks like in order to get the maximum of y. You can see that the two functions y=3f(x) and y=f(2x) are just f(x) with some operations.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.03f(x) will have same x value as minium , but the y value will be multiplied by 3

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0for 3f(x) > minium ( 3 , 15 ) , methinks , havent taught much about it so might not be right

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0For the first function (y=3f(x)), the minimum will occur at the same point x=3, but the value will change by 3 times. That's the minimum point will be (3,15).

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0for f(2x) , one thinks use chain rule

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0let g(x) = f(2x) g'(x) = 2 f ' (2x) =0 for min/max. f ' (2x) =0 gets a bit strange here

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Well, there is no need to use the chain rule, I guess.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0we know that f' (3) =0 also , but I am not 100% sure if that means 2x =3 , dont think it does

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0for the function y=f(2x), the minimum occur at 2x=3 that's x=3/2. The yvalue remains the same. The minimum point, then, is (3/2,5).

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0but with the second one, shouldn't it stretch the y axis??? and the first one th x axis???

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Thinking of it as "stretching" may lead to confusion, but let's go with that metaphor.  The first one divides y by 3: $$y=3f(x) \implies \frac{y}{3} = f(x) $$ Therefore this is actually a shrinking of the yaxis, relative to the function that says the same size. Since the function stays the same size, everything gets bigger, which is why you multiply by 3 to get the minimum.  The second one multiplies x by 2. This is indeed a stretching of the xaxis, meaning the function gets smaller. That's why you divide the x value by two to get the location of the new minimum.
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