If f x - a log e - x - bx 2- x has extremum at x -1 and x -3- thenA- a-3 - 4- b-1 - 8B- a-3 - 4- b-1 - 8C- None of theseD- a-3 - 4- b-1 - 8

The correct option is A a = 3/4, b= 1/8For x gt; 0 or x lt; 0 f'(x) = a/x + 2bx + 1 ∵ f'(1) = 0 ⇒ a + 2b + 1 = 0 and f'(3) = 0 ⇒a/3 + 6b + 1 = 0 Solv ...

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard XII

Mathematics

Extrema

If f x = a lo...

Question

If $f (x) = a l o g_{e} | x | + b x^{2} + x$ has extremum at x = 1 and x = 3, then

a = -3/4, b= -1/8

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

a=3/4, b= -1/8

No worries! We‘ve got your back. Try BYJU‘S free classes today!

a =-3/4, b=1/8

No worries! We‘ve got your back. Try BYJU‘S free classes today!

None of these

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is A
a = -3/4, b= -1/8

For $x > 0 o r x < 0 f^{'} (x) = \frac{a}{x} + 2 b x + 1 ∵ f^{'} (1) = 0 \Rightarrow a + 2 b + 1 = 0 a n d f^{'} (3) = 0 \Rightarrow \frac{a}{3} + 6 b + 1 = 0$
Solving Eqs. (i) and (ii), we get
a = - 3/4, b = -1/8

Suggest Corrections

Similar questions

If $f (x) = a l o g_{e} | x | + b x^{2} + x$ has extremum at x = 1 and x = 3, then

Q. If

\int x^{5} (1 + x^{3})^{\frac{2}{3}} d x = A (1 + x^{3})^{\frac{8}{3}} + B (1 + x^{3})^{\frac{5}{3}} + C, t h e n

Q. If

{log}_{0.2} (x - 1) > {log}_{0.04} (x + 5)

then

Q. If

f (x) = a {log}_{e} | x | + b x^{2} + x

has extremum at

x = 1

and

x = 3

, then

Q. If

f (x) = a {log}_{e} | x | + b x^{2} + x

has extremums at

x = 1

and

x = 3

then

Join BYJU'S Learning Program

If f(x)=a loge |x|+bx2+x has extremum at x = 1 and x = 3, then

The correct option is A a = -3/4, b= -1/8For x>0 or x<0f′(x)=ax+2bx+1∵f′(1)=0⇒a+2b+1=0and f′(3)=0⇒a3+6b+1=0 Solving Eqs. (i) and (ii), we get a = - 3/4, b = -1/8

If $f (x) = a l o g_{e} | x | + b x^{2} + x$ has extremum at x = 1 and x = 3, then

The correct option is A
a = -3/4, b= -1/8

For $x > 0 o r x < 0 f^{'} (x) = \frac{a}{x} + 2 b x + 1 ∵ f^{'} (1) = 0 \Rightarrow a + 2 b + 1 = 0 a n d f^{'} (3) = 0 \Rightarrow \frac{a}{3} + 6 b + 1 = 0$
Solving Eqs. (i) and (ii), we get
a = - 3/4, b = -1/8