Introduction Calculus Applications of Derivatives Introduction Questions What is the derivative of the kinetic energy function? What is the derivative of kinetic energy with respect to velocity? What is the derivative of #tanh(x)#? What is the derivative of voltage with respect to time? If a ball is thrown vertically upward from the ground with an initial velocity of 56 feet per second, for how long will the ball be going upward? A baseball diamond is a square with side 90 ft. A batter hits the ball and runs toward first base with a speed of 26 ft/s. At what rate is his distance from second base decreasing when he is halfway to first base? How do you find the velocity and position vectors if you are given that the acceleration vector is #a(t)= (-4 cos (-2t))i + (-4sin (-2t))j + (-2t)k# and the initial velocity is #v(0)=i+k# and the initial position vector is #r(0)= i+j+k#? How high will a ball go if it is thrown vertically upward from a height of 6 feet with an initial velocity of 60 feet per second and the acceleration is -32 feet per second squred? How many seconds will the ball be going upward if a ball is thrown vertically upward from the ground with an initial velocity of 20 feet per second and #a(t)= -32# feet per second squared? How do you show that the linearization of #f(x) = (1+x)^k# at x=0 is #L(x) = 1+kx#? How do you find the linearization of #f(x)=x^(3/4)# at x=1? Question #e6569 The velocity of a particule is v = 2t + cos (2t). When t = k the acceleration is 0. Show that k = pi/4? Applications of Derivatives View all chapters Introduction Solving Optimization Problems Using the Tangent Line to Approximate Function Values Using Newton's Method to Approximate Solutions to Equations Using Implicit Differentiation to Solve Related Rates Problems Next