Application of Derivatives Test

Result

Application of Derivatives Test - 5

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Weekly Quiz Competition

Question 1
1 / -0

The function f (x) = a x + b is strict increasing for all x ∈ R if

A
a < 0

B
a > 0

C
a = 0

D
none of these

Solution

Since f ‘(x ) = a, therefore, f(x) is strictly increasing on R if a >0.
Question 2
1 / -0

The function f (x ) = a x + b is strict decreasing for all x ∈ R if

A
a> 0

B
a = 0

C
a<0

D
none of these

Solution

Since f ‘(x ) = a, therefore, f ( x ) is strictly decreasing on R if a<0.
Question 3
1 / -0

The function f (x) = x² - 2x is strict decreasing in the interval

A
R

B
( −∞, 1)

C
[1,∞)

D
none of these

E
`

Solution

f ‘ (x ) = 2x – 2 = 2 ( x - 1) <0 if x < 1 i.e. x x∈ (−∞,1). Hence f is strict decreasing in(−∞,1)
Question 4
1 / -0

The equation of the normal to the curve y = sinx at (0, 0) is

A
x + y = 0

B
y = 0

C
x – y = 0

D
x = 0

Solution

Since , dy/dx = cos x, therefore , slope of tangent at ( 0 , 0 ) = cos 0 = 1 and hence slope of normal at ( 0 , 0 ) is - 1 .

Equation of normal at (0,0) is,

y - 0 = slope of normal ×( x - 0)

y = -1(x)

x + y = 0
Question 5
1 / -0

The normal to the curve x = a (cosθ + θ sinθ),y = a (sinθ − θ cosθ) at any point θ is such that

A
it is at a constant distance from the origin

B
it makes a constant angle with X – axis

C
it passes through the origin

D
none of these

Solution

Equation of normal at θ is xcosθ + ysinθ − a = 0. So,normal is at a fixed distance a from the origin.