If f x - y - f x - f y -2 xy -6 for all x - y - R and f -0-2- then y - f x will beA- EllipseB- CircleC- Straight lineD- Parabola

The correct option is D Parabola f^'(x) = n → 0limf(x+h) f(x+0)/h =n → 0limf(x)+f(h)+2xh 6 f(x) f(0)+6/h =2x+n → 0limf(0+h) f(0)/h=2x+f^'(0) f(x)=x^2+2x+C, ...

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

Byju's Answer

Standard XII

Mathematics

Definition of Circle

If f x + y = ...

Question

If f(x+y)=f(x) + f(y) + 2xy - 6 for all $x, y ϵ R$ and f'(0) = 2, then y = f(x) will be

Straight line

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

Parabola

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

Ellipse

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

Circle

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

Open in App

Solution

The correct option is B Parabola
$f^{^{'}} (x) = l i m n \to 0 \frac{f (x + h) - f (x + 0)}{h} = l i m n \to 0 \frac{f (x) + f (h) + 2 x h - 6 - f (x) - f (0) + 6}{h} = 2 x + l i m n \to 0 \frac{f (0 + h) - f (0)}{h} = 2 x + f^{^{'}} (0) f (x) = x^{2} + 2 x + C$ , but f(0)=6
So, $f (x) = x^{2} + 2 x + 6$

Suggest Corrections

Similar questions

Q. If f(x + y) = f(x) + f(y) + 2xy - 6 for all

x, y ϵ R

and f'(0) = 2, then y = f(x) will be

Q. Let

f (x + y) = f (x) + f (y) + 2 x y - 1 \forall x, y \in R .

f (x)

is differentiable for

\forall x \in R

and

f^{'} (0) = sin ϕ

, then

Q. Let

f

be a differentiable function such that

f (x + y) = f (x) + f (y) + 2 x y - 1

for all real

x

and

y

. If

f^{'} (0) = cos α

, then

\forall x \in R

Q. Let

f (x + y) = f (x) + f (y) + 2 x y - 1 \forall x, y \in R

. If

f (x)

is differentiable and

f^{'} (0) = sin ϕ

, then

Q. Let

f (x + y) = f (x) \times f (y)

for all

x

and

y

and

f (7) = 5, f^{'} (0) = 2

then

f^{'} (7)

will be

Join BYJU'S Learning Program

If f(x+y)=f(x) + f(y) + 2xy - 6 for all x,yϵR and f'(0) = 2, then y = f(x) will be

The correct option is B Parabola f′(x)=limn→0f(x+h)−f(x+0)h=limn→0f(x)+f(h)+2xh−6−f(x)−f(0)+6h=2x+limn→0f(0+h)−f(0)h=2x+f′(0)f(x)=x2+2x+C, but f(0)=6 So, f(x)=x2+2x+6

If f(x+y)=f(x) + f(y) + 2xy - 6 for all $x, y ϵ R$ and f'(0) = 2, then y = f(x) will be