Interpreting Derivatives as Slope of Curves

What does the notation f' (f prime) represent?

• The minimum value of the function

• The maximum value of the function

• The derivative of the function

• The integral of the function

What is the slope of the tangent line at a point on a curve?

• The rate of change of x with respect to y

• The rate of change of y with respect to x

• The integral of the curve

• The area under the curve

How does the steepness of a non-linear curve change?

• It remains constant

• It changes constantly

• It only increases

• It only decreases

If delta y is 2 and delta x is 1, what is the slope of the tangent line?

• 1

• 2

• 0.5

• 3

What does a negative slope indicate about the function's behavior?

• The function has a maximum point

• The function is increasing

• The function is decreasing

• The function is constant

What is the slope of the tangent line at the bottom of a curve where y is not increasing or decreasing?

• Positive

• Negative

• Undefined

• Zero

What is the approximate derivative of g at x = 4?

• 1

• 0

• -1

• -3

What is the approximate derivative of g at x = 6?

• 1

• -3

• 0

• -1

Which derivative is greater, g' at 4 or g' at 6?

• Cannot be determined

• They are equal

• g' at 6

• g' at 4

What type of curve is being analyzed in the comparison of derivatives at different points?

• Exponential

• Sinusoidal

• Quadratic

• Linear