Question

8. Let $f$ and $g$ be inverse functions that are differentiable for all $x$. If $f(-5) = 7$ and $g'(7) = 3$, which of the following statements must be false? I. $f'(3) = - II. $f'(-5) = III. $f'(7) = rac{1}{3}$ (A) I only (B) II only (C) III only (D) I and III only

          8.
Let $f$ and $g$ be inverse functions that are differentiable for all $x$. If $f(-5) = 7$ and $g'(7) = 3$, which of the
following statements must be false?
I. $f'(3) = -
II. $f'(-5) = 
III. $f'(7) = rac{1}{3}$
(A) I only
(B) II only
(C) III only
(D) I and III only

8.
Let f and g be inverse functions that are differentiable for all x. If f(-5) = 7 and g'(7) = 3, which of the
following statements must be false?
I. f'(3) = -
II.f'(-5) =
III. f'(7) = rac13
(A) I only
(B) II only
(C) III only
(D) I and III only

Added by Scott M.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Lucas Finney

Step 1

Taking the derivative of both sides of the equation g(f(x)) = x with respect to x, we get g'(f(x)) * f'(x) = 1. We know that f(-5) = 7 and g'(7) = 3. So, if we plug these values into the equation, we get 3 * f'(-5) = 1. Solving for f'(-5), we get f'(-5) = 1/3. Show more…

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Let f and g be inverse functions that are differentiable for all x. If f(-5)=7 and g^(')(7)=3, which of the following statements must be false? I. f^(')(3)=-(1)/(3) II. f^(')(-5)=(1)/(3) III. f^(')(7)=(1)/(3) (A) I only (B) II only (C) III only (D) I and III only 8. Let f and g be inverse functions that are differentiable for all c. If f-5=7 and g7=3,which of the following statements must be false? 1.f(3= 1 11.f(5= 33 A) Ionly BII only CIII only (D)I and III only