Curve + tangent

By "where do they solve it", I mean "where are the solutions?" You've found them. There's really only one step left. What do you suppose that is?

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Originally Posted by Ackbeet

By "where do they solve it", I mean "where are the solutions?" You've found them. There's really only one step left. What do you suppose that is?

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provide a general solution?
show that these values of x satisfy the original equation?

You've found the locations where the line y = x equals the original function. But how do you know that, at those points, y = x touches the original function?

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Originally Posted by Ackbeet

You've found the locations where the line y = x equals the original function. But how do you know that, at those points, y = x touches the original function?

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at the points where y=x touches the original function the gradients are equal

True... but how do you know that?

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Originally Posted by Ackbeet

True... but how do you know that?

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ermm.. because the line y=x is a tangent to the curve? Thus at the point where it is a tangent its gradient is equal to that of the curve?

I'm sorry Im doing really bad with this one!

Hint: evaluate the _____________ at the points of touching, and show that they're all equal to __ .

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Originally Posted by Ackbeet

Hint: evaluate the _____________ at the points of touching, and show that they're all equal to __ .

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evaluate the gradient at the points of touching, and show that they're all equal to 1?

ie. when x = 5pi/2, dy/dx = 1
when x = 9pi/2, dy/dx = 1
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You got it. I would say that once you've shown all that, you're done with this problem.

Thank you soooo much! You've been such a great help :)

You're very welcome. Have a good one!