Trying to find the right answer to this..

Name: Zigya - For The Curious Learner
Rating: 4.4 (740 reviews)

Let x 1 , x 2 ∊ R and let x 1 < x 2 Now x 1 < x 2 ⇒ 7 x 1 , < 7 x 2 ⇒ 7 x 1 – 3 < 7 x 2 , – 3 ⇒ f (x 1 ) < f (x 2 ) ∴ f is strictly increasing function in R.

Previous Year Papers

Download Solved Question Papers Free for Offline Practice and view Solutions Online.

Test Series

Take Zigya Full and Sectional Test Series. Time it out for real assessment and get your results instantly.

Test Yourself

Practice and master your preparation for a specific topic or chapter. Check you scores at the end of the test.

Application of Derivatives

Multiple Choice Questions

131.

The slope of the normal to the curve y = 2 x² + 3 sin x at x = 0 is

3
$1 third$
-3
-3

84 Views

132.

The line y = x + 1 is a tangent to the curve y ² = 4x at the point

(1, 2)
(2, 3)
(1, -2)
(1, -2)

75 Views

133. The normal at the point (1, 1) on the curve 2y + x² = 3 is

x + y = 0
x – y = 0
x + y + 1 = 0
x + y + 1 = 0

114 Views

134. The normal to the curve x² = 4 y passing (1, 2) is

x + y = 3
x – y = 3
x + y = 1
x + y = 1

95 Views

Short Answer Type

135. Show that the function f (x) = 2 x + 3 is a strictly increasing function on R.

85 Views

136. Without using the derivative show that the function f (a) = 7x – 3 is a strictly increasing function on R.

Let x₁, x₂ ∊ R and let x₁< x₂Now x₁ < x₂ ⇒ 7 x₁, < 7 x₂ ⇒ 7 x₁ – 3 < 7 x₂, – 3
⇒ f (x₁) < f (x₂)
∴ f is strictly increasing function in R.

85 Views

137. Show that the function f (x) = x² is an increasing function in (0, ∞).

81 Views

138.

Show that the function f(x) = x² is a decreasing function in (– ∞ 0).

84 Views

139.

Construct an example of a functions which is strictly increasing but whose derivative vanishes at a point in the domain of definition of the function.

82 Views

140.

Prove that the exponential function e^x is strictly increasing on R.

86 Views