Derivative or Antiderivative?

Suppose you were given an equation that describes the velocity of an object, what do you need to do to find the position of the object?

• Find the derivative with respect to time.

• Find the antiderivative with respect to time

• Find the derivative with respect to distance

• Find the antiderivative with respect to distance

What is the derivative of position going to be with respect to time?

• The acceleration

• The jerk

• The velocity

• The integral of jerk

What is needed to find the derivative of the function? (Select all that applies)

• The function

• Finding the derivative with respect to the variable that causes it to change

• The integral

• The secant line that expresses the function

What is the constant for the integral of the function v(t) = 3t²+4, when the position when t = 1 is 5?

What is the slope of the function f(x) = 3x²+4 when x = 2?

Suppose you are on an airplane going 300 mph east and your friend is on another plane going 400 mph south. You both left the airport at the same time. After an hour has passed, at what rate is the distance between the two planes changing? (don't forget the units)

If you are given a line that is tangent to a graph, what might that represent?

• The slope at that point

• The antiderivative

• The secant line

• The derivative

If you are given a square and you are to find the area, that is the same thing as finding.....

• The area under the curve.

• The integral of a linear function/curve

• The area under the curve from a given interval

• The integral of a linear function/curve from a given interval

What is the main idea of finding the antiderivative of a curve without saying it's to find the area under the curve?

Which of the following is the antiderivative of the function f(x) = 3t +5t²+x?

• (x²/2)+C

• 3tx+5t²x +C

• 0

• 3tx+5t²x +(x²/2)+C