Station #1 - HILLGROVE



Station #1

Derivatives – tables

Use the table of values to calculate the derivative of the given function at x = 2.

|x |f(x) |g(x) |f’(x) |g’(x) |

|2 |5 |4 |-3 |9 |

|4 |3 |2 |-2 |3 |

1. s(x) = 3f(x) – 2g(x) 2. H(x) = f(x)g(x)

3. R(x) = [pic] 4. G(x) = f(g(x))

5. F(x) = f(g(2x)) 6. K(x) = f(x2)

1. -27 2. 33

3. [pic] 4. -18

5. -18 6. -8

Station #2

Derivatives

Calculate y’

1. y = (x + 2)8(x + 3)6 2. y = [pic]

3. [pic] 4. y = [pic]

5. [pic] 6. [pic]

1. [pic]

2. [pic]

3. [pic]

4. [pic]

5. [pic]

6. [pic]

Station #3

Derivatives

Calculate y’

1. y = cot(3x2 + 5) 2. [pic]

3. y = [pic] 4. y = (1 – x-1)-1

5. [pic] 6. [pic]

1. [pic]

2. [pic]

3. [pic]

4. [pic] [pic]

5. [pic]

6. [pic]

Station #4

Derivatives

Calculate y’

1. y = x3 + 5x + 4 2. y = sin([pic])

3. [pic] 4. y = xcos(2x)

5. [pic] 6. [pic]

1. [pic]

2. [pic]

3. [pic]

4. [pic]

5. [pic]

6. [pic]

Station #5

Applications

1. Find an equation of the tangent line to the curve

y = [pic] at the point (2, 1)

2. Find an equation of the tangent line to the curve [pic] when x = [pic]

3. Find an equation for the tangent to the graph of [pic]

1. y – 1 = [pic](x – 2)

2. [pic]

3. [pic]

Station #6

Derivatives

Differentiate.

1. [pic] 2. y = sec(2x)

3. y = [pic] 4. [pic]

5. [pic] 6. y = [pic]

1. [pic]

2. [pic]

3. [pic]

4. [pic]

5. [pic]

6. [pic]

Station #6

Limits

1. Evaluate each limit.

a. [pic] b. [pic]

c. [pic] d. [pic]

2. Find a function f and a number a such that

[pic]

1. a. 4

b. 2

c. 4

d. 0

2. [pic]

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