Advertisements
Advertisements
प्रश्न
A function f is said to be increasing at a point c if ______.
पर्याय
f'(c) = 0
f'(c) > 0
f'(c) < 0
f'(c) = 1
Advertisements
उत्तर
A function f is said to be increasing at a point c if f'(c) > 0.
APPEARS IN
संबंधित प्रश्न
Find the interval in which the following function are increasing or decreasing f(x) = 8 + 36x + 3x2 − 2x3 ?
Find the interval in which the following function are increasing or decreasing \[f\left( x \right) = \frac{x^4}{4} + \frac{2}{3} x^3 - \frac{5}{2} x^2 - 6x + 7\] ?
Find the interval in which the following function are increasing or decreasing f(x) = \[5 x^\frac{3}{2} - 3 x^\frac{5}{2}\] x > 0 ?
Show that the function f(x) = sin (2x + π/4) is decreasing on (3π/8, 5π/8) ?
Write the set of values of 'a' for which f(x) = loga x is decreasing in its domain ?
Find the set of values of 'a' for which f(x) = x + cos x + ax + b is increasing on R ?
Function f(x) = 2x3 − 9x2 + 12x + 29 is monotonically decreasing when
If the function f(x) = kx3 − 9x2 + 9x + 3 is monotonically increasing in every interval, then
Show that the function f given by f(x) = tan–1 (sin x + cos x) is decreasing for all \[x \in \left( \frac{\pi}{4}, \frac{\pi}{2} \right) .\]
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).
Find the values of x for which the following functions are strictly decreasing : f(x) = x3 – 9x2 + 24x + 12
Choose the correct option from the given alternatives :
Let f(x) = x3 – 6x2 + 9x + 18, then f(x) is strictly decreasing in ______.
Find the value of x such that f(x) is decreasing function.
f(x) = x4 − 2x3 + 1
Find the values of x for which the function f(x) = 2x3 – 6x2 + 6x + 24 is strictly increasing
The function f(x) = `x - 1/x`, x ∈ R, x ≠ 0 is increasing
State whether the following statement is True or False:
If the function f(x) = x2 + 2x – 5 is an increasing function, then x < – 1
Show that the function f(x) = `(x - 2)/(x + 1)`, x ≠ – 1 is increasing
The sides of a square are increasing at the rate of 0.2 cm/sec. When the side is 25cm long, its area is increasing at the rate of ______
If f(x) = `x^(3/2) (3x - 10)`, x ≥ 0, then f(x) is increasing in ______.
Show that f(x) = 2x + cot–1x + `log(sqrt(1 + x^2) - x)` is increasing in R
Let the f : R → R be defined by f (x) = 2x + cosx, then f : ______.
The function which is neither decreasing nor increasing in `(pi/2,(3pi)/2)` is ____________.
Function given by f(x) = sin x is strictly increasing in.
If f(x) = x + cosx – a then ______.
y = log x satisfies for x > 1, the inequality ______.
Let \[x_0\] be in the domain of a real-valued function \[f\]. When is \[f\] increasing at \[x_0\]?
If \[f'(x)<0\] throughout an interval, then \[f\] is
For \[f(x)=x^3-3x^2+4x\], what is \[f'(x)\]?
For \[f'(x)=12(x-3)(x+2)\], what is the nature of \[f\] on \[(-2,3)\]?
