Question

If the derivative of the function f(x) = {bx?
(bx2 + ax + 4, x>-1
ax2 + b
is everywhere continuous, then the value of 'a' and 'b' are
XS-1
2
O (A) a = 2;b = 3
O (B) a = 3:0 = 2
0 (C) a = -3;b = -2
0 (D) a = 2;b = -3
​

Answer 1

Answer:

If the derivative of the function f(x) = {bx?

(bx2 + ax + 4, x>-1

ax2 + b

is everywhere continuous, then the value of 'a' and 'b' are

XS-1

2

O (A) a = 2;b = 3

O (B) a = 3:0 = 2

0 (C) a = -3;b = -2

0 (D) a = 2;b = -3

Answer 2

first pick the value for LHL and RHL

in these question value OF LHL IS AX^2+B

VALUE OF RHL IS BX^2+AX+4

THEN PUT THE VALUE (-1)

B(-1)^2+A(-1)+4=A(-1)^2+B

b-a+4=a+b

2a=4

a=2

then derivative of f(x)

2bx+a=2ax

put value of x= -1

2b(-1)+a=2a(-1)

-2b+a= -2a

b=3a/2

put value of a i.e a=2

b=3×2/2

b=3

so option (A) IS RIGHT ANSWER