Instantaneous Rate Quickly Problem: Use the pattern in to find quickly the instantaneous rate of change of f(x) = 5x2 51x + 17 at x = 3. Is f (x) increasing or decreasing at this value of x? How can you tell? The Derivative Function: The derivative function is the function that gives the instantaneous rate of change of a given function at any x-value. The name derivative is used because its equation can be derived from the given equation. In 7, g is the derivative function of function f. For polynomial functions, the derivative function can be found as described in the box. When you study calculus, youll learn how to derive this property. Property: Derivative Function of a Polynomial Function If f(x) = xn , where n stands for a nonnegative integer, then f (x) = nxn1. Verbally: To find the derivative of a power function, multiply by the original exponent and decrease the exponent by 1. If f(x) = anxn + . . . + a1x + a0, where the coefficients are real numbers and the exponents are nonnegative integers, then f (x) = an(nxn1 ) + . . . + a1. Verbally: To find the derivative of a polynomial function, take the derivative of each term, multiplying by the coefficient of that term.

Chapter 7: Energy Balance and Weight Control Section 7.1: Energy Balance • Energy balance: the energy you take in (food) matches the energy you put out (calorie burn) - Positive energy balance: when you eat more calories than you burn. - Negative energy balance: when you eat fewer calories than you burn. • Basal metabolism (BMR): the minimum amount of calories the body needs to support itself in a fasting state (not eating). - 1 kcal/kg for men per hour - .9 kcal/kg for women per hour • Resting metabolism: the amount of calories the body uses when a person hasn’t eaten for 4 hours. • Thermic effect of food: when your metabolism is increased during the absorption, digestion, and metabolism of carbs, proteins, and fats. • Bom