Difference between revisions of "Practice problems/A challenging tangent line problem"
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#Is there a point $Q=(x_{1},y_{1})$ on the line $y=x$ such that there is ONLY one tangent line to the curve $y=f(x)$ passing through Q? | #Is there a point $Q=(x_{1},y_{1})$ on the line $y=x$ such that there is ONLY one tangent line to the curve $y=f(x)$ passing through Q? | ||
Justify your answer. | Justify your answer. | ||
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Revision as of 13:36, 11 June 2014
For the following questions, consider the function $$y = f(x) = (x+2)^2.$$
- Find the equations of all lines tangent to $y=f(x)$ that pass through the point $(1,1)$. Note that this point is not on the graph of $f$.
- Is there a point $Q=(x_{1},y_{1})$ on the line $y=x$ such that there is ONLY one tangent line to the curve $y=f(x)$ passing through Q?
Justify your answer.
