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

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

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

9. MATH 101- term 101 : CALCULUS I – Dr. Faisal Fairag

10. MATH 101- term 101 : CALCULUS I – Dr. Faisal Fairag
H(a,b)

11. MATH 101- term 101 : CALCULUS I – Dr. Faisal Fairag

12. MATH 101- term 101 : CALCULUS I – Dr. Faisal Fairag

13. MATH 101- term 101 : CALCULUS I – Dr. Faisal Fairag

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