6. (10 point) Find
where C is the arc of the circle x² + y² = 1 from (1, 0) counterclockwise to ().

(a) (7 point) ∫ tan⁻¹ x dx

(b) (8 point)dy dx

4. (5) if z = f⁻¹(y) = y5 + y3, what is (f⁻¹)'(2)?

5. (15) Find all the local maximum values (局部極大值), local minimum values(局部極小值), and saddle points (鞍點), of the following functionf(x, y) = x3 + y3 + 3x² - 3y² - 8.

7. (10 point) Find dy/dx if y is a differentiable function of x satisfying the equation2x³ + y3 - 5xy = 0.

(a) If f' is continuous, and if the graph of f passes through the points (1, 2) and (3, 5),what is f'(x) dx?

(b) Let F(x) = f(t) dt. What is F'(x)?

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