Rate of Change Skills

Calculate the derivative of f(x) = 3x^2 - 2x + 5.

• f'(x) = 6x - 2

• f'(x) = 3x^2 - 2

• f'(x) = 6x + 2

• f'(x) = 3x^2 - 2x + 5

Explain the interpretation of the slope of a tangent line to a curve at a specific point.

• The slope of a tangent line is the area under the curve at that point

• The slope of a tangent line represents the curvature of the curve

• The interpretation of the slope of a tangent line to a curve at a specific point is the rate of change of the curve at that point.

• The slope of a tangent line indicates the maximum value of the curve

Evaluate the limit lim(x->2) (x^2 - 4) / (x - 2).

• 4

• 2

• 6

• 0

Analyze the instantaneous velocity of an object moving along a straight line given its position function.

• Subtract the final position from the initial position and divide by the time elapsed.

• Differentiate the position function with respect to time to get the velocity function. Evaluate the velocity function at the desired time to find the instantaneous velocity.

• Use the average velocity over a large time interval as the instantaneous velocity.

• Integrate the position function with respect to time to get the velocity function.

Solve a real-world rate problem involving the instantaneous rate of change.

• Use the average rate of change over a large interval as the instantaneous rate of change.

• Estimate the rate of change by randomly selecting a point on the graph.

• Ignore the function representing the rate of change and directly calculate the instantaneous rate.

• Identify the function representing the rate of change, calculate its derivative, and evaluate it at the desired point to find the instantaneous rate of change.