1. Sec 2.7: DERIVATIVES AND RATES OF CHANGE Example: Find the derivative of the function at x = 2. Find Example: Find the derivative of the function at a. Find

2. Sec 2.7: DERIVATIVES AND RATES OF CHANGE Example: Find the derivative of the function at a. Find

3. Sec 2.7: DERIVATIVES AND RATES OF CHANGE an equivalent way of stating the definition of the derivative

4. Sec 2.7: DERIVATIVES AND RATES OF CHANGE The slope of the tangent line at the point (a,f(a)) Tangent line at x=3 Slope of this line

5. Sec 2.7: DERIVATIVES AND RATES OF CHANGE

6. RATES OF CHANGE Chane in x = Chane in y = increment in x average rate of change of y with respect to x over the interval [x1,x2] x= time, y = distance average velocity

7. Sec 2.7: DERIVATIVES AND RATES OF CHANGE RATES OF CHANGE average rate of change of y with respect to x over the interval [x1,x2] instantaneous rate of change = x= time, y = distance instantaneous velocity

8. Sec 2.7: DERIVATIVES AND RATES OF CHANGE RATES OF CHANGE average rate of change of y with respect to x over the interval [x1,x2] instantaneous rate of change =

9. Sec 2.7: DERIVATIVES AND RATES OF CHANGE SUMMARY Two definitions 1 slope of the tangent at x = a 2 average rate of change 3 instantaneous rate of change 4

10. Term 102

14. MATH 101- term 101 : CALCULUS I – Dr. Faisal Fairag H R

15. H R R H (a,b)

16. MATH 101- term 101 : CALCULUS I – Dr. Faisal Fairag H H H H R R

17. H