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State when a function f(x) is said to be increasing on an interval [a, b]. Test whether the function f(x) = x2 − 6x + 3 is increasing on the interval [4, 6] ?
Concept: undefined >> undefined
Show that f(x) = sin x − cos x is an increasing function on (−π/4, π/4)?
Concept: undefined >> undefined
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Show that f(x) = tan−1 x − x is a decreasing function on R ?
Concept: undefined >> undefined
Determine whether f(x) = −x/2 + sin x is increasing or decreasing on (−π/3, π/3) ?
Concept: undefined >> undefined
Find the intervals in which f(x) = log (1 + x) −\[\frac{x}{1 + x}\] is increasing or decreasing ?
Concept: undefined >> undefined
Find the intervals in which f(x) = (x + 2) e−x is increasing or decreasing ?
Concept: undefined >> undefined
Show that the function f given by f(x) = 10x is increasing for all x ?
Concept: undefined >> undefined
Prove that the function f given by f(x) = x − [x] is increasing in (0, 1) ?
Concept: undefined >> undefined
Prove that the following function is increasing on R f \[(x) =\]3 \[x^5\] + 40 \[x^3\] + 240\[x\] ?
Concept: undefined >> undefined
Prove that the following function is increasing on R f \[f\left( x \right) = 4 x^3 - 18 x^2 + 27x - 27\] ?
Concept: undefined >> undefined
Prove that the function f given by f(x) = log cos x is strictly increasing on (−π/2, 0) and strictly decreasing on (0, π/2) ?
Concept: undefined >> undefined
Prove that the function f given by f(x) = x3 − 3x2 + 4x is strictly increasing on R ?
Concept: undefined >> undefined
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
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
