Trying to find the right answer to this..

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

Let x 1 , x 2 x ∊ R and let x 1 < x 2 Now x 1 < x 2 ⇒ a x 1 < a x 2: [ ∵ a > 0] ⇒ a x 1 + b < a x 2 + b ⇒ (x 1 ) < f (x 2 ) ∴ x 1 < x 2 ⇒ f (x 1 ) < f (x 2 ) ⇒ f is a 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

Short Answer Type

141.

Show that the function given by f(x) = e^2x is strictly increasing on R.

127 Views

142.
Prove that f (x) = ax + b, where a and b are constants and a > 0 is an strictly increasing function for all real values of x. without using the derivative.

Let x₁ , x₂ x ∊ R and let x₁ < x₂Now x₁ < x₂⇒ a x₁ < a x_2: [ ∵ a > 0]
⇒ a x₁+ b < a x₂+ b ⇒ (x₁) < f (x₂)
∴ x₁ < x₂ ⇒ f (x₁) < f (x₂)
⇒ f is a strictly increasing function in R.

88 Views

143.

Prove that the logarithmic function is increasing wherever it is defined.

86 Views

144.

Show that the function f given by f (x) = 10^x is increasing for all x.

85 Views

145.

Prove that the function f(x) = x³ – 3x² + 3x – 100 is increasing on R.

88 Views

146.

Prove that the function f(x) = x³ – 3x² + 3x – 100 is increasing on R.

90 Views

147. Prove that the function f (x) = 4x³ – 6x² + 3x + 12 is increasing on R

94 Views

148. Show that the function f given by f(x) = x³ – 3x² + 4x , x ∊ R is strictly increasing on R.

95 Views

Long Answer Type

149.

Prove that the function f (x) = sinx is
(i) strictly increasing in $open parentheses 0 comma space straight pi over 2 close parentheses$
(ii) strictly decreasing in $open parentheses straight pi over 2 comma space straight pi close parentheses$
(iii) neither increasing nor decreasing in $left parenthesis 0 comma space straight pi right parenthesis$ .

88 Views

Short Answer Type

150.

Prove that the function f (x) = cos x is
(i) strictly increasing in $left parenthesis negative straight pi comma space 0 right parenthesis$
(ii) strictly decreasing in $left parenthesis 0 comma space straight pi right parenthesis$
(iii) neither increasing nor decreasing in $left parenthesis negative straight pi comma space straight pi right parenthesis$