# MCQ: Application of derivative

1. Equation of normal to the curve where it cuts x – axis; is

(A) x + y = 1
(B) x – y = 1
(C) x + y = 0
(D) None of these

1. If y = a ln |x| + bx2 + x has its extreme values at x = -1 and x = 2 then P ≡ (a , b) is

(A) (2 , -1)
(B) (2 , -1/2)
(C) (-2 , 1/2)
(D) none of these

1. f(x) = tan-1 (sinx + cosx) is an increasing function in

(A)  (–π/2, 0)
(B) (0, π/2)
(C) (-π/4, π/4)
(D) none of these.

1. If the parabola y2 = 4x meets a circle with centre at (6,5) orthogonally, then possible point (s) of intersection can be;

(A) (4, 4)
(B) (9, 4)
(C) (2, √8)
(D) (3, 2)

1. If f (x) = xa log x and f(0) = 0, then the value of a for which Rolle’s theorem can be applied in [0, 1] is

(A) -2
(B) -1
(C) 0
(D)  1/2

1. In [0, 1] Lagranges Mean Value theorem is NOT applicable to

(A) f(x) =
(B) f(x) =
(C) f(x)  = x|x|
(D) f(x) = |x|

1. For what value of ‘a’ does the curve f(x) = (a2 -2a -2 ) + cosx  is always strictly monotonic for all x ∈ R

(A) a ∈ R
(B) a > 0
(C) 1-√2 < a < 1 + √2
(D) None of these

1. If the curves a x2 + b y2 = 1 and a1 x2 + b1 y2 = 1 intersect orthogonally then

(A)1/a – 1/b = 1/a1 + 1/b1
(B)1/a + 1/b = 1/a1 + 1/b1
(C)1/a + 1/b = 1/a1 + 1/b1
(D) none of these

1. If the equation x5 – 10a3 x2 + b4 x + c5 = 0 has three equal roots,  then

(A) 2b2 –10 a3b2+c5 = 0
(B) 6a5 + c5 = 0
(C) 2c5 –10 a3b2+ b4c5 = 0
(D) b4 = 15 a5

1. The function f is a differentiable function and satisfies the functional equation f(x) + f(y) = f(x + y) – xy – 1for every pair x, y of real numbers. If f(1) = 1, then the number of integers n ≠ 1 for which f(n) = n is

(A) 0
(B) 1
(C) 2
(D) 3