Sample Exam

1. Let f(x)=(x^{3} + 6x + 7)^{1/3}.

- Find f(2)
- Show that f(x) is an increasing function on

(c)Let g be the inverse of f. Evaluate g'(3).

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2. Find f(x)when

a)

b)

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3. Evaluate

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4. A curve passes through the point (1, 4) and has the property that its slope at every point P (on the curve) is twice the y coordinate of P. Find the equation of the curve.

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5. Let

Evaluate f'(p /4).

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6. Using the fact that y = arctan(x) if and only if x = tan(y), along with implicit differentiation,prove that

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7. Find

8.a Find

b. Prove that for any positive integer n

- Use part (b) to evaluate

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