If the slope of the curve y=axb−xat the point (1, 1) is 2 then values of a and b respectively
A
1, -2
No worries! We‘ve got your back. Try BYJU‘S free classes today!
B
-1, 2
No worries! We‘ve got your back. Try BYJU‘S free classes today!
C
1, 2
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
D
2,7
No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution
The correct option is C
1, 2
We have, y=axb−x ⇒=dydx=(b−x)a−ax(−1)(b−x2)=ab(b−x)2 ∴[dydx](1,1)=ab(b−1)2(given)....(1) Since the curve passes through the point (1,1), therefore, 1=ab−1⇒a=b−1 On putting a=b-1 in equation (1), we get (b−1)b(b−1)2=2⇒b=2.∴1=2−1=1. Hence a =1, b=2 Hence (c) is the correct answer.