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hi Slide,Originally Posted by Slide_Rule
How would you find the tangent if you didn't know the function?
I thought of a way but it's rather labourious and not exact.
E.g.: Find the tangent to the inverse of the curve y=x-1/e^x at the point x=a on the inverse curve.
dx/dy=1+1/e^y
solve a=x-1/e^x for x, now use this x value for your y value on the inverse function's derivative so that you can find the gradient, then use point-gradient formula.
The non-exactness comes from the transcendental equation a=x-1/e^x.
yes i'm certain of it... they will not give you the 'x' value, only the 'y' one.Originally Posted by Slide_Rule
So you think they would give you the y value instead?
uhuh, if you're only given the 'x' coordinate, then by 3u techniques only an estimate for the gradient is obtainable.Originally Posted by Slide_Rule
Giving the you x value would be an interesting question. It would probably need to be structured such that you find an approximation to the root of the transcendental equation it produces, though, before hand (through Newton's or bisection method).
you don't need to find the inverse function in order to draw a sketch of its graph - you just reflect the original function in y=x.Originally Posted by rsingh
No it's a question I found in a past trial paper, they ask you to find the inverse function and sketch them both.
I can't remember which trial paper it was from, but that was definetly it.
So is there a logical way of doing this question, or is it meant to be an extremely difficult question?