Question

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??

Answer 1

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.

Answer 2

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

Answer 3

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

Answer 4

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).

Answer 5

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

Answer 6

let g(x) = f(2x)

g'(x) = 2 f ' (2x) =0 for min/max.

f ' (2x) =0

gets a bit strange here

Answer 7

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

Answer 8

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

Answer 9

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).

Answer 10

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

Answer 11

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.

Answer 12

ok, thanks :)