Find the coordinates of the point(s) at which the tangent to the curve

\begin{equation*} y=3x^2+5x-7 \end{equation*}

is parallel to the $x-$axis.

I don't know how to solve this.. help!

  • $\begingroup$ The tangent is parallel to x-axis at the point where $ \frac{dy}{dx}=0$ $\endgroup$ – Pratyush May 6 '15 at 11:35
  • $\begingroup$ Hint: can you find the coordinates of the top of the parabola, even without knowing derivatives? $\endgroup$ – Nicky Hekster May 6 '15 at 11:36

The slope of the tangent line is the derivative. What is the slope of any line parallel to the $x$-axis? Can you use these two facts to deduce an answer?


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