If the functions f(x)=(x3/3)+2 b x+(a x2/2) and g(x)=(x3/3)+a x+b x2, a ≠ 2 b have a common extreme point, then a+2 b+7 is equal to:

Question

If the functions f(x)=(x3/3)+2 b x+(a x2/2) and g(x)=(x3/3)+a x+b x2, a ≠ 2 b have a common extreme point, then a+2 b+7 is equal to: (A) (3/2) (B) 3 (C) 6 (D) 4

Tardigrade Admin · Accepted Answer

f prime(x)=x2+2 b+a x g prime(x)=x2+a+2 b x (2 b-a)-x(2 b-a)=0 ∴ x=1 is the common root Put x=1 text in f prime(x)=0 text or g prime(x)=0 1+2 b+a=0 7+2 b+a=6

Q. If the functions $f (x) = \frac{x ^{3}}{3} + 2 b x + \frac{a x ^{2}}{2}$ and $g (x) = \frac{x ^{3}}{3} + a x + b x^{2}, a \neq = 2 b$ have a common extreme point, then $a + 2 b + 7$ is equal to:

$\frac{3}{2}$

3

6

4

$f^{'} (x) = x^{2} + 2 b + a x$
$g^{'} (x) = x^{2} + a + 2 b x$
$(2 b - a) - x (2 b - a) = 0$
$∴ x = 1$ is the common root
Put $x = 1 in f^{'} (x) = 0 or g^{'} (x) = 0$
$1 + 2 b + a = 0$
$7 + 2 b + a = 6$

Q. If the functions f(x)=3x3​+2bx+2ax2​ and g(x)=3x3​+ax+bx2,a=2b have a common extreme point, then a+2b+7 is equal to:

23​

3

6

4

f′(x)=x2+2b+ax g′(x)=x2+a+2bx (2b−a)−x(2b−a)=0 ∴x=1 is the common root Put x=1 in f′(x)=0 or g′(x)=0 1+2b+a=0 7+2b+a=6

Q. If the functions $f (x) = \frac{x ^{3}}{3} + 2 b x + \frac{a x ^{2}}{2}$ and $g (x) = \frac{x ^{3}}{3} + a x + b x^{2}, a \neq = 2 b$ have a common extreme point, then $a + 2 b + 7$ is equal to:

$\frac{3}{2}$

$f^{'} (x) = x^{2} + 2 b + a x$
$g^{'} (x) = x^{2} + a + 2 b x$
$(2 b - a) - x (2 b - a) = 0$
$∴ x = 1$ is the common root
Put $x = 1 in f^{'} (x) = 0 or g^{'} (x) = 0$
$1 + 2 b + a = 0$
$7 + 2 b + a = 6$