7Rules: Theorem 3.1 Theorem 3.2 Theorem 3.3 For any integer n > 0, For any constant c,Theorem 3.2Theorem 3.3For any integer n > 0,
8Enough, STOP THE DRUM ROLL!!!!! DRUM ROLL PLEASE…..Enough, STOP THE DRUM ROLL!!!!!Theorem 3.4For any real number r,
9Sum and Difference Rules If f(x) and g(x) are differentiable at x and c is any constant, then:
10Examples:Suppose that the height of a skydiver t seconds after jumping from an airplane is given by f(t) = 225 – 20t – 16t2 feet. Find the person’s acceleration at time t.First compute the derivative of this function to find the velocitySecond compute the derivative of this function to find the accelerationThe speed in the downward direction increases 32 ft/s every second due to gravity.
11Given f(x) = x3 – 6x2 + 1a) Find the equation of the tangent line to the curve at x = 1y = -9x + 5b) Find all points where the curve has a horizontal tangentX=0 and x = 4