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Show that f(x) = tan−1 (sin x + cos x) is a decreasing function on the interval (π/4, π/2) ?
Concept: undefined >> undefined
Show that the function f(x) = sin (2x + π/4) is decreasing on (3π/8, 5π/8) ?
Concept: undefined >> undefined
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Show that the function f(x) = cot \[-\] l(sinx + cosx) is decreasing on \[\left( 0, \frac{\pi}{4} \right)\] and increasing on \[\left( 0, \frac{\pi}{4} \right)\] ?
Concept: undefined >> undefined
Show that f(x) = (x − 1) ex + 1 is an increasing function for all x > 0 ?
Concept: undefined >> undefined
Show that the function x2 − x + 1 is neither increasing nor decreasing on (0, 1) ?
Concept: undefined >> undefined
Show that f(x) = x9 + 4x7 + 11 is an increasing function for all x ∈ R ?
Concept: undefined >> undefined
Prove that the function f(x) = x3 − 6x2 + 12x − 18 is increasing on R ?
Concept: undefined >> undefined
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
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
