Question: Is it true that if f(x) is a function and L is the line with equation y= -1 then L cannot be tangent to the graph of f(x) at more than one point?

Question

anonymous · Answer

Can you think of a function that y=-1 is tangent to in more than one place?

anonymous · Answer

sinx

anonymous · Answer

what therom would be applied here to prove its false?

anonymous · Answer

intermediate value?

anonymous · Answer

its called a contradiction or contrapositive
proof by contradiction is what we are looking for here

anonymous · Answer

can you think of a function that has the x axis as a tangent in two places?

anonymous · Answer

f(x) = (x+1)^2(x-1)^2 -1.this has 2 local minimums at y=-1 , thus tangent to f(x) at 2 points

anonymous · Answer

well there you go then, you proved the statement is wrong

anonymous · Answer

what is the definition of proof by contradiction