Derivatives of Inverse Functions Gift 2004

DERIVATIVES OF INVERSE FUNCTIONS

1. Let gx=x5+3x-2 and let g-1 denote the inverse of g. Then g-1'(2) is equal to:

(A) 183 (B) 18 (C) 1 (D) 8

2. Let fx=14x3+x-1 and let f-1 denote the inverse of f. Then f-1'(3) is equal to

(A) 431 (B) 16 (C) 14 (D) 13

3. Let fx=x5+x. Find the value of ddxf-1(x) at x = 2.

(A) 81 (B) 6 (C) -16 (D) 16

4. Let hx=x3+2x-1 and let h-1 denote the inverse of h. Then h-1'(2) is equal to:

(A) 14 (B) 5 (C) 15 (D) 114

5. If f(4)=5 and f'4=23, then calculate: f-1'(5).

(A) 15 (B) 14 (C) 23 (D) 32

6. If g(7)=3 and g'3=56 and g'7=34 , then g-1'3= ?

(A) 34 (B) 56 (C) 17 (D) 43

7. Let fx=3x4+x and let g be the inverse function of f What is the value of g’(2)?

(A) 12 (B) -111 (C) 111 (D) 113

8. Let fx=x5+1 and let g be the inverse function of f. What is the value of ’(0) ?

(A) -1 (B) 15 (C) g’(0) does not exist

(D) g’(0) cannot be determined from the given information.

9. The following table shows the values of differentiable functions f and g.

If Hx=f-1(x) then H’(3) equals

(A) -116 (B) 1 (C) -12 (D) 12

10. The following table shows the values of differentiable functions f and g.

If Hx=f-1(x) then H’(1) equals

(A) 1 (B) 0 (C) -1 (D) 12

11. Let fx=x3-4x and let f-1 denote the inverse of f. Then f-1'(6) is equal to:

(A) 113 (B) 16 (C) 112 (D) -112

12. Let hx=x-4 and let h-1 denote the inverse of h. Then h-1'(2) is equal to:

(A) 14 (B) 18 (C) 8 (D) 4

13. Let fx=sinx, -π2≤x≤π2, and let g be the inverse function of f.

What is the value of '12 ?

(A) 23 (B) 32 (C) 6π (D) 2

14. Let gx=2x3-x2+1 Find the value of ddxg-1(x) at x = 13.

(A) 120 (B) 113 (C) 13 (D) 20

15. If h(2)=-3, h'2=14 and h'(-3)=13 compute h-1'(-3) .

(A) 14 (B) 13 (C) 4 (D) 3