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Higher maths!!

Can someone help me with this differentiation question?

Calculate f’(4) given that f(x) = (2x^2 - 2) / root x

Sorry I couldn’t upload an image so it looks even more confusing written out. I thought the root x would have moved up to become -2x^-1/2
But all I know is the answer is 49/8 and I have no clue how to get that!! I thought differentiation was easy so I’m stressing
Reply 1
Original post by RaggaMuffin49
Can someone help me with this differentiation question?
Calculate f’(4) given that f(x) = (2x^2 - 2) / root x
Sorry I couldn’t upload an image so it looks even more confusing written out. I thought the root x would have moved up to become -2x^-1/2
But all I know is the answer is 49/8 and I have no clue how to get that!! I thought differentiation was easy so I’m stressing

I’m doing National 5 maths but from what I know,

For example if it says

F(x) = 3x + 7
Find the value of f(3)
You would then substitute the x for 3.
This means it would be
F(x)= 3(3) + 7
F(x)= 9 + 7
F(x)= 16


If however, it gives you an answer
For example if it says
F(x)=3x - 10
F(a)= -31. Find value of a
you would then do
3x - 10 = -31
(+10 to both sides)
3x = -21
(Divide by 3)
x= -7

Hope that helps, I have no clue how to do it if it’s not functions.
Reply 2
Original post by LSK104
I’m doing National 5 maths but from what I know,
For example if it says
F(x) = 3x + 7
Find the value of f(3)
You would then substitute the x for 3.
This means it would be
F(x)= 3(3) + 7
F(x)= 9 + 7
F(x)= 16
If however, it gives you an answer
For example if it says
F(x)=3x - 10
F(a)= -31. Find value of a
you would then do
3x - 10 = -31
(+10 to both sides)
3x = -21
(Divide by 3)
x= -7
Hope that helps, I have no clue how to do it if it’s not functions.

sadly that is not the answer as it involves the derivate of the function
Reply 3
where is this question from is it from a higher paper?
Reply 4
Original post by raggamuffin49
Can someone help me with this differentiation question?
Calculate f’(4) given that f(x) = (2x^2 - 2) / root x
Sorry I couldn’t upload an image so it looks even more confusing written out. I thought the root x would have moved up to become -2x^-1/2
But all I know is the answer is 49/8 and I have no clue how to get that!! I thought differentiation was easy so I’m stressing

Using index rules, when you divide by x^(1/2) you multiply (the whole numerator) by x^(-1/2), so use that to elminate the fraction and youre left with a relatively simple expression which can be differentiated as usual and then evaulate it when x=4.
(edited 2 months ago)
Reply 5
Original post by Blenxo
where is this question from is it from a higher paper?

https://www.highermathematics.co.uk/wp-content/uploads/2022/10/ESEP-3-Final.pdf
Reply 6

It probably would have been a better idea to post the link originally instead of describe the q 😂
Original post by RaggaMuffin49
Can someone help me with this differentiation question?
Calculate f’(4) given that f(x) = (2x^2 - 2) / root x
Sorry I couldn’t upload an image so it looks even more confusing written out. I thought the root x would have moved up to become -2x^-1/2
But all I know is the answer is 49/8 and I have no clue how to get that!! I thought differentiation was easy so I’m stressing
If you find out I’d appreciate it! I’d say move the root x up to a power of a half, differentiate it so its 4x - x^-1/2, 4x4 is 16, 4 to the power of a -1/2 isn’t a whole number however so Im unsure how to continue to get 49/8! 49/16 is also not a whole number so Im unsure it they’ve times both numbers or not
Reply 8
Original post by RaggaMuffin49
Can someone help me with this differentiation question?
Calculate f’(4) given that f(x) = (2x^2 - 2) / root x
Sorry I couldn’t upload an image so it looks even more confusing written out. I thought the root x would have moved up to become -2x^-1/2
But all I know is the answer is 49/8 and I have no clue how to get that!! I thought differentiation was easy so I’m stressing

Separate f(x) into two fractions. (2x^2)/root x -2/root x . Simplify the indices and then proceed as normal with the differentiation then sub in x = 4 after differentiating.

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