Let a, b R be such that the function f given by f(x)=ln∣x∣+bx2+ax,x=0has extreme values at x=1and x=2.Statement 1: f has local maximum at x=1and at x=2.Statement 2: a=21andb=4−1

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Let a, b R be such that the function f given by $f (x) = ln ∣ x ∣ + b x^{2} + a x, x \neq = 0$ has extreme values at $x = 1$ and $x = 2$ .Statement 1: f has local maximum at $x = 1$ and at $x = 2$ .Statement 2: $a = \frac{1}{2} and b = \frac{- 1}{4}$

Statement 1 is false, statement 2 is true

Statement 1 is true, statement 2 is true; statement 2 is a correct explanation for statement 1

Statement 1 is true, statement 2 is true; statement 2 is not a correct explanation for statement 1

Statement 1 is true, statement 2 is false

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Let a, b R be such that the function f given by

f (x) = ln ∣ x ∣ + b x^{2} + a x, x \neq = 0

has extreme values at

x = 1

and

x = 2

.Statement 1: f has local maximum at

x = 1

and at

x = 2

.Statement 2:

a = \frac{1}{2} and b = \frac{- 1}{4}

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Question Text	Let a, b R be such that the function f given by $f (x) = ln ∣ x ∣ + b x^{2} + a x, x \neq = 0$ has extreme values at $x = 1$ and $x = 2$ .Statement 1: f has local maximum at $x = 1$ and at $x = 2$ .Statement 2: $a = \frac{1}{2} and b = \frac{- 1}{4}$
Answer Type	Video solution: 1
Upvotes	150

Let a, b R be such that the function f given by f(x)=ln∣x∣+bx2+ax,x=0has extreme values at x=1and x=2.Statement 1: f has local maximum at x=1and at x=2.Statement 2: a=21​andb=4−1​

Filo tutor solutions (1)

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Let a, b R be such that the function f given by $f (x) = ln ∣ x ∣ + b x^{2} + a x, x \neq = 0$ has extreme values at $x = 1$ and $x = 2$ .Statement 1: f has local maximum at $x = 1$ and at $x = 2$ .Statement 2: $a = \frac{1}{2} and b = \frac{- 1}{4}$