Applications of Differentiation

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Question

Applications of Differentiation

Consider the function f(x)= 2sin(x) + [(sqrt3)/2] x² This function has two inflection numbers A<B in [0,2pi]:

A= and B= For each of the following intervals, tell whether f(x) is concave up (type in CU) or concave down (type in CD).

[0,A)=

(A,B)=

(B,2pi]=

calculus Differentiation math

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Answer 1

Answer #1

f(x)=cosx +(√2 /2)x

f '(x)=-sinx+(√2 /2)

for critical numbers f '(x)=0

-sinx+(√2 /2)=0

sinx=(√2 /2)

x=pi/4 ,3pi/4

A=pi/4

B=3pi/4

f "(x)=-cosx

f "(pi/4)=-cos(pi/4)= -(√2 /2) <0

f "(3pi/4)=-cos(3pi/4)= (√2 /2) >0

f(x) has a localmaximum at A and a local minimum at B

answered by: ANURANJAN SARSAM

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Answer 2

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Applications of Differentiation

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