Tangent and Normal Part 17 - Application of Derivatives - Diploma Maths - II

TL;DR

Find the coordinates at which the tangent of the curve y = x^3 - 3x + 1 is parallel to the x-axis.

Transcript

click the Bell icon to get latest videos from ekeeda Hello friends in this video we are going to solve one more problem on tangent and normal let us start with problem number 20 to find the points on the curve y is equal to X cube minus 3x plus 1 at which tangent is parallel to x axis here the given equation of the curve is y is equal to X cube min... Read More

Key Insights

• ☺️ When a tangent is parallel to the x-axis, the slope of the tangent is equal to zero.
• 🥡 The slope of the tangent can be calculated by taking the derivative of the equation of the curve.
• 👈 Setting the derivative equal to zero allows us to find the x-values for the points on the curve where the tangent is parallel to the x-axis.
• ❣️ By substituting the x-values into the equation of the curve, the corresponding y-values can be determined.
• ❣️ The final answer includes the x and y coordinates of the two points where the tangent is parallel to the x-axis.
• ❓ Solving this problem requires knowledge of calculus.
• ☺️ The slope of the x-axis is always zero.
• ❓ Differentiation is used to find the derivative of a function.

Questions & Answers

Q: What is the equation of the given curve?

The equation of the given curve is y = x^3 - 3x + 1.

Q: How can we determine when the slope of the tangent is parallel to the x-axis?

For the slope of the tangent to be parallel to the x-axis, its slope should be equal to zero.

Q: How do we calculate the slope of the tangent?

The slope of the tangent can be calculated by taking the derivative of the equation of the curve with respect to x (dy/dx).

Q: How do we find the x-values for the points on the curve?

By equating the slope of the tangent to zero and solving the resulting equation, the x-values for the points are obtained.

Q: What are the two points on the curve where the tangent is parallel to the x-axis?

The two points are (1, -1) and (-1, 3).

Summary & Key Takeaways

• The given problem asks for the coordinates at which the tangent of the curve is parallel to the x-axis.

• To find these coordinates, the slope of the tangent is set equal to the slope of the x-axis, which is zero.

• By differentiating the equation of the curve and setting the derivative equal to zero, the x-values for the points are found.