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1. (4 points) (a) Differentiate f(x) = 3x2 +

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(1)

Name:

1. (4 points)

(a) Differentiate f (x) = 3x

2

+ x − 1 from the first principles.

(b) Hence find the gradient of tangent line to the graph of f when x = 2.

(c) Find the coordinates of the point on the graph of f , at which the

gradient is −1.

(2)

2. (6 points) Find the second derivative of each of the following functions:

(a) f (x) = xe

2x

(b) g(x) = sin(x

2

+ 1)

(c) h(x) = √

x + ln(sin x)

(3)

3. (4 points) Solve the following equation:

2 cos

3

x = −3 sin x cos x

for 0 ¬ x ¬ 2π.

(4)

4. (6 points) The graph of f (x) is shown below. Use the diagrams to sketch the graph of

(a) g(x) = 1

f (|x|)

(5)

(b) h(x) = [f (x)]

2

− 1

Cytaty

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1. (4 points) (a) Differentiate f(x) = 3x2 +

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