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The family of curves y = kx^3 is known for having:
The family of curves y = kx^3 is known for having:
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Practice Questions
1 question
Q1
The family of curves y = kx^3 is known for having:
One turning point
Two turning points
No turning points
Three turning points
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The cubic function y = kx^3 has one turning point at x = 0.
Questions & Step-by-step Solutions
1 item
Q
Q: The family of curves y = kx^3 is known for having:
Solution:
The cubic function y = kx^3 has one turning point at x = 0.
Steps: 7
Show Steps
Step 1: Understand that the equation y = kx^3 represents a family of cubic functions, where 'k' is a constant that can change the shape of the curve.
Step 2: Recognize that a cubic function can have turning points, which are points where the curve changes direction.
Step 3: To find the turning points, we need to find the derivative of the function y = kx^3.
Step 4: The derivative of y = kx^3 is dy/dx = 3kx^2.
Step 5: Set the derivative equal to zero to find the turning points: 3kx^2 = 0.
Step 6: Solve for x: This equation is zero when x = 0 (since k is a constant and not zero).
Step 7: Conclude that the cubic function y = kx^3 has one turning point at x = 0.
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