Trying to find the right answer to this..

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

Here f (x) = x 2 – 2ax – 6 ∴ f ' (x) = 2x – 2a f (x) is increasing when f ' (x) > 0 ⇒ 2 (x – a) > 0 ⇒ x – > 0 ⇒ x > a But x > 0 ∴ a ∊ (– ∞ , 0)

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

151. Which of the following function are strictly decreasing on

open parentheses 0 comma space straight pi over 2 close parentheses space ?

(a) cos x (b) cos 2x (c) cos 3x (d) tan x

79 Views

152. Show that the function f (x) = x⁷ + 8 x⁵ + 1 is increasing function for all values of x.

88 Views

153.

Show that f (x) = tan ^-¹ (sin x + cos x) is a strictly increasing function in the interval $open parentheses 0 comma space space straight pi over 4 close parentheses$

75 Views

154.

Determine whether $straight g left parenthesis straight x right parenthesis space equals space cos space left parenthesis 2 straight x space plus space straight pi over 4 right parenthesis$ is increasing or decreasing for $fraction numerator 3 straight pi over denominator 8 end fraction less than straight x less than fraction numerator 7 straight pi over denominator 8 end fraction.$

85 Views

155. Prove that the function log sin x is strictly increasing on

open parentheses 0 comma space space straight pi over 2 close parentheses

and strictly decreasing in

open parentheses straight pi over 2 comma space space straight pi close parentheses.

90 Views

156.

Prove that the function f given by f(x) = log cos x is strictly decreasing on $open parentheses 0 comma space straight pi over 2 close parentheses$ and strictly increasing on $open parentheses straight pi over 2 comma space straight pi close parentheses.$

90 Views

157. On which of the following intervals is the function x¹⁰⁰ + sin x – 1 strictly increasing?
(i) (1, 1) (ii) (0, 1) (iii)

open parentheses straight pi over 2 comma space straight pi close parentheses

(iv)

open parentheses 0 comma space space straight pi over 2 close parentheses

86 Views

158.
Find the value of a for which the function f (x) = x³ – 2ax + 6 is increasing for x > 0.

Here f (x) = x² – 2ax – 6
∴ f ' (x) = 2x – 2a
f (x) is increasing when f ' (x) > 0
⇒ 2 (x – a) > 0 ⇒ x – > 0
⇒ x > a
But x > 0
∴ a ∊ (– ∞ , 0)

92 Views

159.

Show that $straight y equals log space left parenthesis 1 plus straight x right parenthesis space minus space fraction numerator 2 straight x over denominator 2 plus straight x end fraction$ is an increasing function of x throughout its domain.