ZFR: I honestly don't completely understand what you mean by "advanced functions way". There are a couple of methods of finding the correct answer without using derivatives, but...
While I don't mind giving homework help over forums in general, this looks like it's a textbook example problem i.e. something you should be able to solve yourself if you're studying this.
Unless you're not studying this and it's for something outside your curriculum?
InaneKorruption: It's a thinking question our teacher gave us because in about two weeks we're starting calculus, but go ahead, hit me with the calculus answer if you can. Any help would be appreciated.
OK, fair enough. With calculus it's extremely easy. But, if it's a thinking question your teacher wants you to solve without using calculus, here is a method:
METHOD 1 (without using derivatives) Consider constructing a circle that is a tangent to that function at that point, then find the tangent to the circle at that point.
Example. Try figuring out the details yourself, I'm sure your teacher will appreciate the work you put this.
Once you do this, you'll really appreciate how much easier it is to do it by learning calculus. Using derivatives:
METHOD 2 (using derivatives) The derivative of the function is:
f'(x) = 3x^2 - 6 (you'll learn why when you start calculus)
So the derivative at the point x=1 is
f'(1) = .... (complete this yourself by substituting x=1 to the equation above)
so the tangent is a line with slope=f'(1) (the value you get above)
Find the value of the function at the point x=1
f(1) = ... (complete this yourself)
So your tangent is a line with slope=f'(1) and passing throuhg the point ( 1, f(1) )
Given the this you should be able to write an equation for the tangent line.
----------------------------- Once you get your tangent equation using either of the methods above, finding intersection points should be trivial (just form an equation).
Hope this is clear.
