Question

Prove that the function f given by f (x) = x² – x + 1 is neither strictly increasing nor strictly decreasing on (– 1, 1).

Answer 1

Step-by-step explanation:

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12th

Maths

Application of Derivatives

Increasing and Decreasing Functions

Show that the function x2 -...

MATHS

Show that the function x

2

−x+1 is neither increasing nor decreasing on (0,1).

December 26, 2019avatar

Samruta Amizz

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ANSWER

Given,

the function f(x)=x

2

−x+1

f(x)=x

2

−x+1

f

′

(x)=2x−1

f

′

(x)>0, ∀x∈(

2

1

,1) [∵f

′

(x)>0⇒ strictly increasing]

f

′

(x)<0,∀x∈(0,

2

1

) [∵f

′

(x)<0⇒ strictly decreasing]

clearly,

we can see that

f(x) is strictly increasing in the interval (

2

1

,1)

f(x) is strictly decreasing in the interval (0,

2

1

)

∴f(x) is neither increasing nor decreasing on the whole interval (0,1)