Question

if f(x)=3x4-4x2+5. then the interval for which f(x) Satisfies all the conditions of Rolle's Theorem Is???.
please give answer with steps​.

Answer 1

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Since, f(x) satisfies the conditions of

Rolle's theorem in [1,2] and f(x) is continuous in [1,2]

⇒f(2)=f(1)

Then using Rolle's theorem, we have

∫

1

2

f

′

(x)dx=[f(x)] 1/2

=f(2)−f(1)=0

∵f(2)=f(1)

Answer 2

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$\bf\underline{\underline{\orange{ Question:-}}}$

if f(x)=3x⁴-4x²+5. then the interval for which f(x) Satisfies all the conditions of Rolle's Theorem Is

$\bf\underline{\underline{\orange{ Answer:-}}}$

Given function is f(x)=3x⁴-4x²+5.

let us check the 3rd condition of Rolle's Theorem

on the given interval

(1). [0,2] ⇒f(0)= 5, f(2)= 37

clearly,f(0) ≠ f(2)

(2). [ -1,1]⇒f(-1)= 4,&f(1)=4

clearly,f(-1) =f(1)

(3). [ -1,0]⇒f(-1)= 4,&f(0)=5

clearly,f(-1) ≠ f(0)

(4). [ 1,2]⇒f(1)= 4,&f(2)=37

clearly,f(1) ≠ f(2)

Hence,Rolle's Theorem is applicable on [ -1,1]

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I hope it will helpful...❤️❤️❤️