Find the points of inflection of the graph of the function. (If an answer does n

ID: 2849310 • Letter: F

Question

Find the points of inflection of the graph of the function. (If an answer does not exist, enter DNE.)

f(x) = 5 sin x + 5 cos x, [0, 2]

Describe the concavity. (Enter your answers using interval notation.)

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Complete two iterations of Newton's Method for the function using the given initial guess. (Round your answers to four decimal places.)

f(x) = x2 6, x1 = 2.7

f(xn)

f'(xn)

(x, y) = (smaller x-value) (x, y) = (larger x-value) concave upward (?,?) concave downward (?,?)

f(x)=5sinx +5cosx

f '(x)=5cosx -5sinx

f ''(x)=-5sinx -5cosx

inflection point ==>f "(x)=0 ==>-5sinx -5cosx =0 ==>x =3pi/4 ,7pi/4

x=3pi/4 ==>f(3pi/4)=5sin(3pi/4) +5cos(3pi/4) =0

x=7pi/4 ==>f(7pi/4)=5sin(7pi/4) +5cos(7pi/4) =0

(x,y)=(3pi/4,0)

(x,y)=(7pi/4,0)

concave upward ==>f "(x)>0

==>-5sinx -5cosx >0

==>5sinx +5cosx <0

==>5sinx<-5cosx

==>sinx<-cosx

==>tanx<-1

==>x=(3pi/4,7pi/4)

concave downward ==>f "(x)<0

==>-5sinx -5cosx <0

==>5sinx +5cosx >0

==>5sinx>-5cosx

==>sinx>-cosx

==>tanx>-1

==>x=[0,3pi/4)U(7pi/4,2pi]

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