How many points of intersection do the curve and the line have?
Answer and explanation
Correct answer: A. exactly one
- Step 1: Set equal: , so .
- Step 2: has a repeated root, so the discriminant is zero.
- Step 3: There is exactly one intersection, at , and the line is a tangent.
Answer
exactly one.
Why not the others: none, because the line lies below the curve: misreads the discriminant, which is zero rather than negative. two, at and : invents a second root: has only . infinitely many, because the equations are equivalent: the two equations are not the same function.
Practise more Graphs of functions.
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