BasCal RETAKE: FINAL EXAM

What does the statement "The derivative of a function f(x) at a point a is the limit of the difference quotient as h approaches 0" define?

• The slope of the tangent line to the curve of f(x) at point a
• The area under the curve of f(x) between points a and b
• The maximum value of f(x) within an interval [a, b]
• The integral of the function f(x) from a to b

Which mathematical concept defines the instantaneous rate of change of a function at a given point?

• Integral
• Derivatives
• Limit
• Exponential Function

A car travels along a winding road, and its position at time is given by the function s(t) = 2t^3 - 3t^2 + 6t, where is measured in meters and is measured in seconds. At t = 2 seconds, what is the velocity of the car?

• 24 m/s
• 18 m/s
• 12 m/s
• 8 m/s

A curve is defined by the function y = x^3 - 2x^2 + 4x - 1. Find the equation of the tangent line to the curve at the point where x = 2 ?

• y = 9x - 17
• y = 10x - 21
• y = 12x - 25
• y = 13x - 29

A curve is defined by the function f(x) = x^2 + 3x - 2. At the point x = 1 , what is the equation of the normal line to the curve?

• y = 3x - 4
• y = 2x + 1
• y = -x + 1
• y = -2x + 3

What is the degree of the differential equation?

• 1st degree
• 2nd cegree
• 3rd degree
• 4th degree

What is the order of the differential equation?

• 1st order
• 2nd order
• 3rd order
• 4th order

• 2nd order
• 3rd order
• 4th order
• 5th order

• x/y
• -x/y
• y/x
• -y/x

What is the 5th derivatives of cos (2x)?

• -16 sin (2x)
• -32 cos (2x)
• 16 sin (2x)
• 32 cos (2x)