How can I find the points on the curve y = x^4 − 10x^2 + 1 where the tangent line is horizontal?
1 Answer
Take the first derivative, set it equal to
Explanation:
The tangent line is horizontal where the derivative is equal to zero.
Graphically interpreted, the derivative at a point on a curve is the slope at that point. We draw tangent lines at certain points to represent the slope at certain points. A horizontal line,
Take the first derivative with the Power Rule, set
So, since
The tangent line is horizontal at
The tangent line is horizontal at
The tangent line is horizontal at