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Karnataka Board PUCPUC Science 2nd PUC Class 12

PUC Science 2nd PUC Class 12 - Karnataka Board PUC Question Bank Solutions for Mathematics

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Find 'a' for which f(x) = a (x + sin x) + a is increasing on R ?

[6] Applications of Derivatives
Chapter: [6] Applications of Derivatives
Concept: undefined >> undefined

Find the values of 'a' for which the function f(x) = sin x − ax + 4 is increasing function on R ?

[6] Applications of Derivatives
Chapter: [6] Applications of Derivatives
Concept: undefined >> undefined

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Find the set of values of 'b' for which f(x) = b (x + cos x) + 4 is decreasing on R ?

[6] Applications of Derivatives
Chapter: [6] Applications of Derivatives
Concept: undefined >> undefined

Find the set of values of 'a' for which f(x) = x + cos x + ax + b is increasing on R ?

[6] Applications of Derivatives
Chapter: [6] Applications of Derivatives
Concept: undefined >> undefined

Write the set of values of k for which f(x) = kx − sin x is increasing on R ?

[6] Applications of Derivatives
Chapter: [6] Applications of Derivatives
Concept: undefined >> undefined

If g (x) is a decreasing function on R and f(x) = tan−1 [g (x)]. State whether f(x) is increasing or decreasing on R ?

[6] Applications of Derivatives
Chapter: [6] Applications of Derivatives
Concept: undefined >> undefined

Write the set of values of a for which the function f(x) = ax + b is decreasing for all x ∈ R ?

[6] Applications of Derivatives
Chapter: [6] Applications of Derivatives
Concept: undefined >> undefined

Write the interval in which f(x) = sin x + cos x, x ∈ [0, π/2] is increasing ?

[6] Applications of Derivatives
Chapter: [6] Applications of Derivatives
Concept: undefined >> undefined

State whether f(x) = tan x − x is increasing or decreasing its domain ?

[6] Applications of Derivatives
Chapter: [6] Applications of Derivatives
Concept: undefined >> undefined

Write the set of values of a for which f(x) = cos x + a2 x + b is strictly increasing on R ?

[6] Applications of Derivatives
Chapter: [6] Applications of Derivatives
Concept: undefined >> undefined

The interval of increase of the function f(x) = x − ex + tan (2π/7) is

[6] Applications of Derivatives
Chapter: [6] Applications of Derivatives
Concept: undefined >> undefined

The function f(x) = cot−1 x + x increases in the interval

[6] Applications of Derivatives
Chapter: [6] Applications of Derivatives
Concept: undefined >> undefined

The function f(x) = xx decreases on the interval

[6] Applications of Derivatives
Chapter: [6] Applications of Derivatives
Concept: undefined >> undefined

The function f(x) = 2 log (x − 2) − x2 + 4x + 1 increases on the interval

[6] Applications of Derivatives
Chapter: [6] Applications of Derivatives
Concept: undefined >> undefined

If the function f(x) = 2x2 − kx + 5 is increasing on [1, 2], then k lies in the interval

[6] Applications of Derivatives
Chapter: [6] Applications of Derivatives
Concept: undefined >> undefined

Let f(x) = x3 + ax2 + bx + 5 sin2x be an increasing function on the set R. Then, a and b satisfy.

[6] Applications of Derivatives
Chapter: [6] Applications of Derivatives
Concept: undefined >> undefined

The function \[f\left( x \right) = \log_e \left( x^3 + \sqrt{x^6 + 1} \right)\] is of the following types:

[6] Applications of Derivatives
Chapter: [6] Applications of Derivatives
Concept: undefined >> undefined

If the function f(x) = 2 tan x + (2a + 1) loge | sec x | + (a − 2) x is increasing on R, then

[6] Applications of Derivatives
Chapter: [6] Applications of Derivatives
Concept: undefined >> undefined

Let \[f\left( x \right) = \tan^{- 1} \left( g\left( x \right) \right),\],where g (x) is monotonically increasing for 0 < x < \[\frac{\pi}{2} .\] Then, f(x) is

[6] Applications of Derivatives
Chapter: [6] Applications of Derivatives
Concept: undefined >> undefined

Let f(x) = x3 − 6x2 + 15x + 3. Then,

[6] Applications of Derivatives
Chapter: [6] Applications of Derivatives
Concept: undefined >> undefined
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