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

1. anonymous

You 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.

2. anonymous

3f(x) will have same x value as minium , but the y value will be multiplied by 3

3. anonymous

for 3f(x) -> minium ( 3 , 15 ) , methinks , havent taught much about it so might not be right

4. anonymous

For 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).

5. anonymous

for f(2x) , one thinks use chain rule

6. anonymous

let g(x) = f(2x) g'(x) = 2 f ' (2x) =0 for min/max. f ' (2x) =0 gets a bit strange here

7. anonymous

Well, there is no need to use the chain rule, I guess.

8. anonymous

we know that f' (3) =0 also , but I am not 100% sure if that means 2x =3 , dont think it does

9. anonymous

for the function y=f(2x), the minimum occur at 2x=3 that's x=3/2. The y-value remains the same. The minimum point, then, is (3/2,5).

10. anonymous

but with the second one, shouldn't it stretch the y axis??? and the first one th x axis???

11. anonymous

Thinking 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 y-axis, 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 x-axis, meaning the function gets smaller. That's why you divide the x value by two to get the location of the new minimum.

12. anonymous

ok, thanks :)