Application of Derivatives - Online Test
Q1. The function f (x) = a x + b is strict increasing for all x∈Riff
Answer : Option C
Explaination / Solution:
Since f ‘ (x ) = a , therefore , f ( x ) is strict increasing on R iff a >0
Q2.
The function f (x) = is strict decreasing in the interval
Answer : Option D
Explaination / Solution:
f ‘ (x )=2x – 2 = 2 ( x - 1) <0 if x < 1 i.e. x x∈(−∞,1). Hence f is strict decreasing in left decreasing in(−∞,1)
Q3. For the curve tangent is parallel to X – axis where
Answer : Option D
Explaination / Solution:
dydx=0⇒dydt=0⇒2t−1=0⇒t=12.
Q4. The equation of the normal to the curve y = sinx at (0, 0) is
Answer : Option C
Explaination / Solution:
Since , therefore , slope of tangent at ( 0 , 0 ) = cos 0 = 1 and hence slope of normal at ( 0 , 0 ) is - 1 .
Q5.
The tangent to the parabola at the point makes with the X – axis an angle of
Answer : Option D
Explaination / Solution:
Therefore , slope of tangent at ( 1 , ½ ) = 1. Hence , required angle is
Therefore , slope of tangent at ( 1 , ½ ) = 1. Hence , required angle is
Q6. The curve y = is inclined at to the X – axis at (0, 0) but it touches X – axis at (1, 0) , then the values of a, b, c, are given by
Answer : Option B
Explaination / Solution:
At ( 0 , 0) , slope of tangent = = 1. c = 1. At ( 1 ,0 ) , slope of tangent = 0.3a+2b+c=0. Also, when x = 1 , y = 0 , therefore , a + b + c = 0
At ( 0 , 0) , slope of tangent = = 1. c = 1. At ( 1 ,0 ) , slope of tangent = 0.3a+2b+c=0. Also, when x = 1 , y = 0 , therefore , a + b + c = 0
Q7. The normal to the curve x = a (cosθ+θsinθ),y = a (sinθ−θcosθ)at any point θ is such that
Answer : Option A
Explaination / Solution:
Equation of normal at θisxcosθ+ysinθ−a=0.So,normal is at a fixed distance a from the origin.
Q8.
The normal to the curve 2 y = 3 – at (1, 1) is
Answer : Option C
Explaination / Solution:
Q9. The equation of the tangent to the curve at the point is
Answer : Option B
Explaination / Solution:
Q10. The equation of the tangent to the curve at the point (0, 1) is
Answer : Option B
Explaination / Solution:
