JEE PYQ: Application Of Derivatives Question 61
Question 61 - 2019 (09 Apr Shift 1)
If the tangent to the curve $y = x^3 + ax - b$ at the point $(1, -5)$ is perpendicular to the line $-x + y + 4 = 0$, then which one of the following points lies on the curve?
(1) $(-2, 1)$
(2) $(-2, 2)$
(3) $(2, -1)$
(4) $(2, -2)$
Show Answer
Answer: (4)
Solution
Slope of tangent $= -1$. $y’(1) = 3 + a = -1 \Rightarrow a = -4$. Point $(1,-5)$: $1 - 4 - b = -5 \Rightarrow b = 2$. Curve: $y = x^3 - 4x - 2$. At $(2, -2)$: $8 - 8 - 2 = -2$. Verified.
BETA
