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    How do you decide whether to differentiate or to do 'change in y/change in x' to find the gradient?

    For example, in the question below I know you can differentiate and whatnot to find the gradient but I don't see why you can't do change in y/change in x with the coordinates on the x-axis (despite the fact that 0 would be in the numerator)?

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    You can't use \frac{\Delta y}{\Delta x} between the roots, because this doesn't give you the gradient of the normal(AB isn't perpendicular to the curve).
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    Because it is a normal to point A so it does not go through point b. So you only have point A to work with so you must therefore use differentiation.

    Hope this helps

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    (Original post by ImNervous)
    Because it is a normal to point A so it does not go through point b. So you only have point A to work with so you must therefore use differentiation.

    Hope this helps

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    Ah that makes sense, thank you!
 
 
 
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