# Practice Zone Maths : Application of Derivative

1. Let f(x) = x – sinx and g(x) = x – tanx where x∈ (0, π/2) . Then for these values of x ;

(A) f(x). g(x)>0
(B) f(x) g(x) <0
(C)f(x)/ g(x)>0
(D) none of these

1. If f (x) = x3 + bx2 + cx + d and 0 < b2 < c, then in (-∞ , ∞)

(A) f (x) is a strictly increasing function
(B) f(x) has a local maxima
(C) f(x) is a strictly decreasing function
(D) f(x) is bounded

1. If f(x) = 1 + x/1! + x2/2! + x3/3! …………+ xn/n! , then f(x) = 0 (n is odd , n≥3)

(A)  can’t have any real root
(B)  can’t have any repeated  root
(C)  has one positive root
(D)  none of these

1. If f (x) = sin x + a2x + b is an increasing function for all values of x, then

(A) a ∈ (-∞,-1)
(B) a ∈ R
(C) a ∈ (-1 , 1)
(D) none of these

1. If f(x)= x2e-x2/a2 is an increasing function then (for a > 0), x lies in the interval

(A) [a , 2a]
(B) (-∞,  -a] ∪ [0 ,  a]
(C) (-a, 0)
(D) None of these

1. Let f(x) = |x-1| + |x-2| + |x-3| + |x-4| ∀x ∈ R . Then

(A) x = 2 is the point of local minima
(B) x = 3 is the point of local minima
(C) x = 1 is the point of local minima
(D) none of these

1. If a, b are real numbers such that x3-ax2 + bx – 6 = 0 has its roots real and positive then minimum value of b is

(A) 1
(B) 2
(C) 3(36)1/3
(D) None of these

1. If f'(x) exists for all x∈R and g(x) = f(x) – (f(x))2 + (f(x))3 ∀ x ∈R , then

(A)g(x) is increasing whenever ‘f’ is increasing
(B)g(x) is increasing whenever ‘f’ is decreasing
(C)g(x) is decreasing whenever ‘f’ is increasing
(D)none of these

1. Cosine of the angle of intersection of curves y = 3x1 logx and y = xx -1 is

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

1. The equation 8x3 – ax2 + bx –1 = 0 has three real roots in G.P. If λ1 ≤ a ≤ λ2 , then ordered  pair  (λ1,  λ2) can be

(A) (-2, 2)
(B) (18, 12)
(C) (-10, -8)
(D) none of these