Question

Find a if the slope of tangent to the curve y= ax²+b at (½,0) is -1.​

Answer 1

Step-by-step explanation:

xy+ax+by=2 ----- ( 1 )

On differentiating both sides w.r.t. x, we get

x

dx

dy

+y+a+b

dx

dy

=0

⇒

dx

dy

(x+b)=−a−y

⇒

dx

dy

=

x+b

−a−y

Now,

The slope of the tangent =2

(

dx

dy

)

(1,1)

=2

⇒

1+b

−a−1

=2

⇒ −a−1=2+2b

⇒ −a=3+2b

⇒ a=−(3+2b)

On substituting a=−(3+2b),x=1 and y=1 in equation ( 1 ), we get

⇒ 1−(3+2b)+b=2

⇒ 1−3−2b+b=2

⇒ b=−4

And

⇒ a=−(3+2b)=−(3−8)=5

∴ a=5 and b=−4