Sec 2.7: DERIVATIVES AND RATES OF CHANGE

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Presentation transcript:

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

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

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

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

Sec 2.7: DERIVATIVES AND RATES OF CHANGE

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

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

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]

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

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

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

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

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

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