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

(b)

2. (5 point) Let g(x) = x(x - 1)(x - 2)(x - 3). How many real roots has the equationg'(x) = 0? For each, specify an interval containing that root and no others.

(a) (7 point) ∫ tan⁻¹ x dx

(b) (8 point)dy dx

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.

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

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)?

一、配合題：【請針對每一題目選擇最適合的搭配選項號碼， 並將答案填寫在答案卷上。如1.( 搭配的選項號碼)、2. ( 搭配的選項號碼)】( 一) 題目1. automatic thoughts 2. family constellation3. unconditional positive regard 4. BASIC- ID5. externalization 6. dream analysis7. body awareness 8. basic anxiety9. basic mistakes 10. circular questions( 二) 搭配的選項1. Reality therapy 2. Existential psychotherapy3. Gestalt therapy 4. Solution- focused therapy5. Adlerian psychotherapy 6. REBT7. Multimodal therapy 8. Family therapy9. Narrative therapy 10. Person- centered therapy11. Psychoanalysis 12. Cognitive therapy13. Psychodrama 14. Transactional Analysis 15. Behavior therapy