Algebra: Differentiation

The video tutorial covers differentiation, focusing on finding dy/dx for a given equation. It explains the rules of differentiation, including dropping the power and reducing it by one. The tutorial then moves on to solving for the range of x values where the curve has a negative gradient, using the quadratic formula. The process involves setting up an inequality and substituting values into the quadratic formula to find critical values. The video emphasizes careful substitution and understanding of differentiation rules to solve calculus problems effectively.

What is the derivative of the function y = x^3 - 2x^2 - 15x + 5?

• 3x^2 - 4x - 15

• 3x^2 - 4x + 5

• 3x^2 + 4x - 15

• 3x^2 - 2x - 15

Which of the following terms is eliminated during differentiation?

• 5

• 2x^2

• 15x

• x^3

What is the first step in finding the range of x values for which the curve has a negative gradient?

• Set the original equation equal to zero

• Set the derivative less than zero

• Set the original equation less than zero

• Set the derivative equal to zero

What is the quadratic formula used to solve the inequality?

• x = (-b ± √(b^2 - 4ac)) / 2a

• x = (b ± √(b^2 + 4ac)) / 2a

• x = (b ± √(b^2 - 4ac)) / 2a

• x = (-b ± √(b^2 + 4ac)) / 2a

What are the critical values obtained from solving the quadratic inequality?

• -5/3 and -3

• -3 and 5/3

• -5/3 and 3

• 3 and 5/3

In which range of x values does the curve have a negative gradient?

• x < -5/3 or x > 3

• x > -5/3 and x < 3

• -5/3 < x < 3

• x < -5/3 and x > 3

How many marks are available for correctly setting up the inequality and solving it?

• 2 marks

• 3 marks

• 4 marks

• 5 marks