Differentiation

[IloveManUtd]

In my question:

Calculate the gradient of the curve y= (x-4)/x when the point is y=3

Do I differentiate the equation of the curve first or do I subsitute y= 3 first. Thx.

 

[mmm4444bot]

Yes, you need to know what the derivative is, before you can evaluate it.

However, you're not going to evaluate y` by substituting 3 for y because the derivative of y does not contain the symbol y.

Did you try anything ?

If you had, perhaps you would have seen that you need to know the value of x when y is 3.

Here are the steps:

(1) Solve the given equation for x, when y = 3

(2) Differentiate the expression for y

(3) Substitute the value for x that you found in step (1) into the expression for y` that you found in step (2)

(4) Simplify

Please show your work, if you need more help with this exercise.

Cheers, Mark

PS: As a check for us both, I think that the gradient (slope) of y's curve is 1, where y = 3.

 

[IloveManUtd]

Thanks Mark for your steps. I got the answer 1. Thx a heap!