C2 differntaion range of a function

find the maximum value and hence the range of values for the function f(x)=27-2x^4

The answer just gives this as 27 and then f(x) is less than or equal to 27

??

Reply 1

refref

What exam board are you on? Domain and range is in C3 on edexcel.

Range is just the range of values that a function can be. In f(x) = 27-2x^4 , your maximum value is 27 therefore there cannot be any values greater than 27. This means that the whole function is less than 27 (In this case it does, not always though).

Picture it as an upside down quadratic that crosses the y axis at 27.

Reply 2

Pickford

11

You should differentiate the function, and it has 1 maximum point. When plotted on a graph it is an upside down parabola.

Differentiate it, set it to 0 to find the min/max points and solve for x. Then substitue this back in the original point and find y. This gives you your maximum point. It can't be any higher then this but it can be every number below so it is less than or equal to your max point.

Reply 3

f45

OP

2

im on dexcel and there's like 1 example and 1 question in the C2 book :smile:

thank you, I thought it was something like that

Reply 4

interlanken-fall

13

Original post by refref

What exam board are you on? Domain and range is in C3 on edexcel.

Range is just the range of values that a function can be. In f(x) = 27-2x^4 , your maximum value is 27 therefore there cannot be any values greater than 27. This means that the whole function is less than 27 (In this case it does, not always though).

Picture it as an upside down quadratic that crosses the y axis at 27.

still a bit confused, so f(x) ≤ 27 is the range as y values less then 27 gives you the range for a maximum parabola?

Reply 5

davros

16

Original post by interlanken-fall

still a bit confused, so f(x) ≤ 27 is the range as y values less then 27 gives you the range for a maximum parabola?

This thread is 11 years old!

Can you plot the function in question, and hence see what;s going on?

Reply 6

interlanken-fall

13

Original post by davros

This thread is 11 years old!

Can you plot the function in question, and hence see what;s going on?

i made a thread
https://www.thestudentroom.co.uk/showthread.php?t=6995556&p=94853067#post94853067
i get it now, can you check if my reasoning is right thank you

Reply 7

the bear

20

all functions which have an even power of x ( and no others ) are U shaped.

the - makes it an upside down U so there will be a maximum point.

C2 differntaion range of a function

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