# Find the coordinates of the point(s) at which the tangent to the curve is parallel to the x-axis.

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!

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