Unit 2 . Taking the derivative of a function using derivative rules - constant rule, power rule, rule sum/difference rule, chain rule, exponential rules, logarithmic rules, product rule, quotient f ( x ) = x8-14 - + 8V/x-4e* +11 g(x) = (In x) (4x2 - 3) h(x) = *2+1 3x k (x ) = 67/x5+1 -e3x + - Applications of derivatives o Writing the equation of a tangent line Find the equation of the tangent to the curve f (x) = vx2 + 3 when x = 1. Find the equation of the tangent line to the curve / (x) =4 3.x+1 when x = -1. o Finding marginal revenue, cost, or profit Physics - relationships between position, velocity, and acceleration Velocity and Acceleration: If a cannonball is shot directly upward, its height above the ground in feet after t seconds is given by s(t) = 256t - 161. Find the velocity function after t seconds. Find the acceleration function after t seconds. What is the maximum height the cannonball reaches? When does the cannonball hit the ground? What is the velocity of the cannonball when it hits the ground? Finding intervals of increasing/decreasing and maximums/minimums using the first derivative f(x) = -2x3 - 9x2+ 108x - 10 5x f ( x) = x2 + 1 Finding intervals of concave up/concave down and points of inflection using the second derivative f(x) = -2x3 -9x2 + 108x -10 5x f (x ) = x2 + 1