Step 3: Continuation Condition 4 - f'(n)=-n =ƒ'(6)=-6<0 The graph is decreasing at x=6 Condition 5 = ⇒ f'(n+4)=n+1 ⇒ƒ'(6+4)=6+1 ⇒ƒ(10)=7>0 The graph is increasing at x = 10 Condition 6 = f(n)=n -ƒ(6)=6 The graph passes through point (6,6) Condition 7 ⇒ƒ(6+4)=6+7 ⇒ƒ(10)=13 The graph passes through point (10,13) Step 4: Draw the graph of the function f(x) The graph of the function f(x) Concave down f" (x)<0 x 6 (6,6) (10, 13) concave up F(x)>0 Concave down x > 10 Step 1: Define the problem The given condtions are • f'(x) <0,x0,nn+4 • f'(n) = -n • f'(n+4)=n+1 • f(n)=n • f(n+4)=n+7 Step 2: Determine the all important points of function with given conditions Given that n = 6 Condition 1 ⇒f" (x) <0,x0,n0,6 10 The graph is concave down over the interval(10,∞) The concavity of graph changes at x=6,10 then these are inflection points of function f(x).

Step 3: Continuation Condition 4 - f'(n)=-n =ƒ'(6)=-6<0 The graph is decreasing at x=6 Condition 5 = ⇒ f'(n+4)=n+1 ⇒ƒ'(6+4)=6+1 ⇒ƒ(10)=7>0 The graph is increasing at x = 10 Condition 6 = f(n)=n -ƒ(6)=6 The graph passes through point (6,6) Condition 7 ⇒ƒ(6+4)=6+7 ⇒ƒ(10)=13 The graph passes through point (10,13) Step 4: Draw the graph of the function f(x) The graph of the function f(x) Concave down f" (x)<0 x 6 (6,6) (10, 13) concave up F(x)>0 Concave down x > 10 Step 1: Define the problem The given condtions are • f'(x) <0,x0,nn+4 • f'(n) = -n • f'(n+4)=n+1 • f(n)=n • f(n+4)=n+7 Step 2: Determine the all important points of function with given conditions Given that n = 6 Condition 1 ⇒f" (x) <0,x0,n0,6 10 The graph is concave down over the interval(10,∞) The concavity of graph changes at x=6,10 then these are inflection points of function f(x).

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter7: Analytic Trigonometry

Section7.6: The Inverse Trigonometric Functions

Problem 93E

See similar textbooks