If velocity is above the x-axis, position in increasing (forward). What do we know about position if the velocity curve is below the x-axis? If velocity is below the x-axis, the position is decreasing (moving backward). What is the derivative of velocity? Acceleration. What is the derivative of position? Velocity. After 7 minutes, the tank is being drained at an instantaneous rate of 3 liters per minute. The slope of the line tangent to the graph of V at t = 7 is equal to -3. The function V gives the volume of liquid in the tank, in liters, after t minutes. What is the best interpretation or the following statement?Ī tank is being drained of water.

If D is the distance driven, D' is the instantaneous rate of change. The function D gives the total distance Eddie has driven (in kilometers) t hours after he left.

*10 is the base What is the best interpretation or the following statement?Įddie drove from New York City to Philadelphia. What is the derivative of a^x? ln(a)a^x How do you change the base of a log? lnx=? log∨e(x) What is the derivative of log∨a(x)? 1/((lna)x) If g(x) = f^(-1)(x), what is g(f(x))? g(f(x)) = x If h is the inverse of f, what is h'(x)? h'(x) = 1/(f'(h(x)) What is the derivative of inverse sine? What are the pythagorean identities? If y = cos^(-1)x, what is x? x = cosy What is the derivative of inverse cosine? What is the derivative of inverse tangent? What is the derivative of logx? 1/((ln10)x) What is the derivative of ln(x)? 1/x (0,∞) What is the derivative of e^x? e^x How does a = e^(lna) The natural log of a is the power you need to raise e to to get to a.

Optimization khan academy