Determine whether Rolle’s Theorem can be applied to f on the closed interval [a,b]. If Rolle’s...

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Determine whether Rolle’s Theorem can be applied to f on the closed interval [a,b]. If Rolle’s theorem can be applied, find all values of c in the open interval (a,b) such that f′(c)=0 F(x) = ∣x – 2∣ - 2 [0,4]

Transcript of Determine whether Rolle’s Theorem can be applied to f on the closed interval [a,b]. If Rolle’s...

Page 1: Determine whether Rolle’s Theorem can be applied to f on the closed interval [a,b]. If Rolle’s theorem can be applied, find all values of c in the open.

Determine whether Rolle’s Theorem can be applied to f on the closed interval [a,b]. If Rolle’s theorem can be applied, find all values of c in the open interval (a,b) such that f′(c)=0

F(x) = ∣x – 2∣ - 2 [0,4]

Page 2: Determine whether Rolle’s Theorem can be applied to f on the closed interval [a,b]. If Rolle’s theorem can be applied, find all values of c in the open.

Find the points, if any, guaranteed by the Mean Value Theorem for the closed interval [a,b]

F(x) = √x – 2x [0,4]

Page 3: Determine whether Rolle’s Theorem can be applied to f on the closed interval [a,b]. If Rolle’s theorem can be applied, find all values of c in the open.

Use the derivative tests to determine any relative extrema

G(x) = 2x²(1-x²)

Page 4: Determine whether Rolle’s Theorem can be applied to f on the closed interval [a,b]. If Rolle’s theorem can be applied, find all values of c in the open.

Sketch the graph of a function f, having the given characteristics:

F(0)=f(6)=0F′(3) = f′(5)=0F′(x)>0 if x<3F′(x) >0 if 3<x<5F′(x) <0 if x>5F′′(x) <0 if x<3 or x>4F′′(x) >0 if 3<x<4

Page 5: Determine whether Rolle’s Theorem can be applied to f on the closed interval [a,b]. If Rolle’s theorem can be applied, find all values of c in the open.

The cost of inventory depends on the ordering and storage costs according to the inventory model:

C = (Q/x)s + (x/2)r

Determine the order size that will minimize the cost, assuming that sales occur at a constant rate, Q is the number of units sold per year, r is the cost of storing one unit for 1 year, s is the cost of placing an order, and x is the number of units per order.

Page 6: Determine whether Rolle’s Theorem can be applied to f on the closed interval [a,b]. If Rolle’s theorem can be applied, find all values of c in the open.

Analyze and sketch the graph of the function:

F(x) = (x-1)³(x-3)²

Page 7: Determine whether Rolle’s Theorem can be applied to f on the closed interval [a,b]. If Rolle’s theorem can be applied, find all values of c in the open.

At noon, ship A is 100 km due east of ship B. Ship A is sailing west at 12 km per hour, and ship B is sailing south at 10 km per hour. At what time will the ships be nearest to each other, and what will this distance be?

Page 8: Determine whether Rolle’s Theorem can be applied to f on the closed interval [a,b]. If Rolle’s theorem can be applied, find all values of c in the open.

Use newton’s method to approximate any real zeros of the function accurate to 3 decimal places. Use the zero finder on calculator to verify.

F(x) = x³ - 3x -1

Page 9: Determine whether Rolle’s Theorem can be applied to f on the closed interval [a,b]. If Rolle’s theorem can be applied, find all values of c in the open.

Use the information to evaluate and compare Δy and dy:

F(x) = x4+1 x=-1 Δx = dx = .01

Page 10: Determine whether Rolle’s Theorem can be applied to f on the closed interval [a,b]. If Rolle’s theorem can be applied, find all values of c in the open.

The diameter of a sphere is measured to be 18 centimeters, with a maximum possible error of .05 cm. Use differentials to approximate the possible propagated error and percent error in calculating the surface area and the volume of the sphere.


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