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How do i answer this differential question?

The curve C has equation y = 4x^2 + (5−x)/ x , x is not 0
The point P on C has x-coordinate 1
. (a) Show that the value of dy dx at P is 3.
(edited 7 years ago)
Differentiate then sub x=1
quotient rule
Reply 3
That is not thorough enough. I need to know how to differentiate the 5-x/x part
Original post by Harry Long
That is not thorough enough. I need to know how to differentiate the 5-x/x part


Separate them as fractions i.e 5/x -x/x
Reply 5
Original post by Mystery.
Separate them as fractions i.e 5/x -x/x


Yeah i got to that. But what next? its basically 5/x - 1 but

how do you do the thing to the power with 5/x because u cant cant u?
Original post by Harry Long
Yeah i got to that. But what next? its basically 5/x - 1 but

how do you do the thing to the power with 5/x because u cant cant u?


5/x would become 5x-1 :smile:
Original post by Harry Long
Yeah i got to that. But what next? its basically 5/x - 1 but

how do you do the thing to the power with 5/x because u cant cant u?


You can. Exponent rule: x^ -n =1/x^n
(edited 7 years ago)
dy/dx = 8x - 5x-2

Now you should be able to finish it off
Reply 9
Aaa nevermind i did it on my own
...
Reply 11
I also need help with this question (c):

(b) Find an equation of the tangent to C at P. [3]
For this i got y = 3x + 5 which is correct
This tangent meets the x-axis at the point (k, 0).

(c) Find the value of k.

how would i do c?

would i make both equations and equal and solve for x (k)
Original post by Harry Long
I also need help with this question (c):

(b) Find an equation of the tangent to C at P. [3]
For this i got y = 3x + 5 which is correct
This tangent meets the x-axis at the point (k, 0).

(c) Find the value of k.

how would i do c?

would i make both equations and equal and solve for x (k)


No sub x and y coordinated of the point given in b and solve for k.
Original post by Harry Long
Aaa nevermind i did it on my own

Congratulations
Reply 14
so sub x = 1 into y = 3x + 5?
For y=3x+5
We have y=0 and x=k essentially as it's (k,0) so make the question into 0 and solve for x this will be your value of k
I'm sure you can do this on your own.
Reply 17
oh i was just confused with the question

now i understand :smile: as my teacher says, once i answer a question fully, i can answer the exact same question again. that is why practising questions for revision is the best instead of just reading and making pretty little notes that have no effect!

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