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Find the interval in which the following function are increasing or decreasing \[f\left( x \right) = \frac{3}{2} x^4 - 4 x^3 - 45 x^2 + 51\] ?
Concept: undefined >> undefined
Find the interval in which the following function are increasing or decreasing \[f\left( x \right) = \log\left( 2 + x \right) - \frac{2x}{2 + x}, x \in R\] ?
Concept: undefined >> undefined
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Determine the values of x for which the function f(x) = x2 − 6x + 9 is increasing or decreasing. Also, find the coordinates of the point on the curve y = x2 − 6x + 9 where the normal is parallel to the line y = x + 5 ?
Concept: undefined >> undefined
Find the intervals in which f(x) = sin x − cos x, where 0 < x < 2π is increasing or decreasing ?
Concept: undefined >> undefined
Show that f(x) = e2x is increasing on R.
Concept: undefined >> undefined
Show that f(x) = e1/x, x ≠ 0 is a decreasing function for all x ≠ 0 ?
Concept: undefined >> undefined
Show that f(x) = loga x, 0 < a < 1 is a decreasing function for all x > 0 ?
Concept: undefined >> undefined
Show that f(x) = sin x is increasing on (0, π/2) and decreasing on (π/2, π) and neither increasing nor decreasing in (0, π) ?
Concept: undefined >> undefined
Show that f(x) = log sin x is increasing on (0, π/2) and decreasing on (π/2, π) ?
Concept: undefined >> undefined
Show that f(x) = x − sin x is increasing for all x ∈ R ?
Concept: undefined >> undefined
Show that f(x) = x3 − 15x2 + 75x − 50 is an increasing function for all x ∈ R ?
Concept: undefined >> undefined
Show that f(x) = cos2 x is a decreasing function on (0, π/2) ?
Concept: undefined >> undefined
Show that f(x) = sin x is an increasing function on (−π/2, π/2) ?
Concept: undefined >> undefined
Show that f(x) = cos x is a decreasing function on (0, π), increasing in (−π, 0) and neither increasing nor decreasing in (−π, π) ?
Concept: undefined >> undefined
Show that f(x) = tan x is an increasing function on (−π/2, π/2) ?
Concept: undefined >> undefined
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
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
