wednesday, january 28, 2015mat 145. wednesday, january 28, 2015mat 145 which of the following...true...
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Calculus I (MAT 145)Dr. Day Wednesday Jan 28,2015
Questions about Limits or Continuity?
Tangent Lines and Derivatives (2.7 & 2.8)
Assignments
Wednesday, January 28, 2015
MAT 145
MAT 145Wednesday, January 28, 2015
Match the expression in the left column (A thru F) with its correct description in the right column (1 thru 6). Explain your determination of each correct match!
MAT 145Wednesday, January 28, 2015
Match the expression in the left column (A thru F) with its correct description in the right column (1 thru 6). Explain your determination of each correct match!
MAT 145Wednesday, January 28, 2015
MAT 145Wednesday, January 28, 2015
A
B
C
D
E
MAT 145Wednesday, January 28, 2015
Calculate the slope at x = −2.
Calculate the slope at x = −1.
Calculate the slope at x = 0.
Calculate the slope at x = a.
MAT 145Wednesday, January 28, 2015
Calculate the slope of f(x) = x2 at x = a.
MAT 145Wednesday, January 28, 2015
We call this slope calculation the
derivative of f at x = a.
MAT 145Wednesday, January 28, 2015
MAT 145Wednesday, January 28, 2015
MAT 145Wednesday, January 28, 2015
MAT 145Wednesday, January 28, 2015
The value f ’(a) is called:• the derivative of f at x =
a,• the instantaneous rate
of change of f at x = a, • the slope of f at x = a,
and• the slope of the
tangent line to f at x = a.
MAT 145Wednesday, January 28, 2015
The derivative in action!
S(t) represents the distance traveled by some object, where t is in minutes and S is in feet. What is the meaning of S’(12)=100?
MAT 145Wednesday, January 28, 2015
The derivative in action!
C(p) represents the total daily cost of operating a hospital, where p is the number of patients and C is in thousands of dollars. What is the meaning of C’(90)=4.5?
MAT 145Wednesday, January 28, 2015
The derivative in action!
V(r) represents the volume of a sphere, where r is the radius of the sphere in cm. What is the meaning of V ’(3)=36π?
MAT 145Wednesday, January 28, 2015
Can we create a derivative function f that will be true for any
x value where a derivative exists?
MAT 145Wednesday, January 28, 2015
MAT 145Wednesday, January 28, 2015
MAT 145Wednesday, January 28, 2015
The slope of this secant line differs from the slope of the tangent line by an amount that is approximately proportional to h. As h approaches zero, the slope of the secant line approaches the slope of the tangent line. Therefore, the true derivative of f at x is the limit of the value of the slope function as the secant lines get closer and closer to being a tangent line.
MAT 145Wednesday, January 28, 2015
Calculate the derivative function, f ’(x), for f(x) = x2. Use the limit definition of the derivative.
MAT 145Wednesday, January 28, 2015
MAT 145
Assignments WebAssign : Sec 2.5: due tonight! Quiz #4: WebAssign
Available NOW! Due by midnight Tuesday, January 27.
Tangent return . . .
Wrapping It Up
Wednesday, January 28, 2015