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Prove that the function f(x) = cos x is:
(i) strictly decreasing in (0, π)
(ii) strictly increasing in (π, 2π)
(iii) neither increasing nor decreasing in (0, 2π).
Concept: undefined >> undefined
Show that f(x) = x2 − x sin x is an increasing function on (0, π/2) ?
Concept: undefined >> undefined
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Find the value(s) of a for which f(x) = x3 − ax is an increasing function on R ?
Concept: undefined >> undefined
Find the values of b for which the function f(x) = sin x − bx + c is a decreasing function on R ?
Concept: undefined >> undefined
Show that f(x) = x + cos x − a is an increasing function on R for all values of a ?
Concept: undefined >> undefined
Let f defined on [0, 1] be twice differentiable such that | f (x) | ≤ 1 for all x ∈ [0, 1]. If f(0) = f(1), then show that | f'(x) | < 1 for all x ∈ [ 0, 1] ?
Concept: undefined >> undefined
Find the interval in which f(x) is increasing or decreasing f(x) = x|x|, x \[\in\] R ?
Concept: undefined >> undefined
Find the interval in which f(x) is increasing or decreasing f(x) = sinx + |sin x|, 0 < x \[\leq 2\pi\] ?
Concept: undefined >> undefined
Find the interval in which f(x) is increasing or decreasing f(x) = sinx(1 + cosx), 0 < x < \[\frac{\pi}{2}\] ?
Concept: undefined >> undefined
What are the values of 'a' for which f(x) = ax is increasing on R ?
Concept: undefined >> undefined
What are the values of 'a' for which f(x) = ax is decreasing on R ?
Concept: undefined >> undefined
Write the set of values of 'a' for which f(x) = loga x is increasing in its domain ?
Concept: undefined >> undefined
Write the set of values of 'a' for which f(x) = loga x is decreasing in its domain ?
Concept: undefined >> undefined
Find 'a' for which f(x) = a (x + sin x) + a is increasing on R ?
Concept: undefined >> undefined
Find the values of 'a' for which the function f(x) = sin x − ax + 4 is increasing function on R ?
Concept: undefined >> undefined
Find the set of values of 'b' for which f(x) = b (x + cos x) + 4 is decreasing on R ?
Concept: undefined >> undefined
Find the set of values of 'a' for which f(x) = x + cos x + ax + b is increasing on R ?
Concept: undefined >> undefined
Write the set of values of k for which f(x) = kx − sin x is increasing on R ?
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 ?
Concept: undefined >> undefined
Write the set of values of a for which the function f(x) = ax + b is decreasing for all x ∈ R ?
Concept: undefined >> undefined
