Calculus – Linear Equations Practice Set · 4

Question:
Find the x-values at which the tangent line to h of x equals 2x cubed minus 12x is horizontal.

Calculus – Linear Equations Practice Set · 4

This lesson shows how to find the x-values where a polynomial curve has a horizontal tangent line by setting the first derivative equal to zero and solving the resulting equation. The power rule is applied to differentiate a cubic function, and the solutions are verified by substitution.

In this lesson, you will learn to:
• Explain why a horizontal tangent line requires the derivative to equal zero
• Apply the power rule to differentiate a cubic polynomial term by term
• Solve a quadratic equation arising from setting the derivative to zero
• Verify solutions by substituting back into the derivative

Course: Calculus
Level: Grade 12

Pause before each step, try the next part yourself, and then continue to check your reasoning.

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