Advertisements
Advertisements
Question
A function f is said to be increasing at a point c if ______.
Options
f'(c) = 0
f'(c) > 0
f'(c) < 0
f'(c) = 1
Advertisements
Solution
A function f is said to be increasing at a point c if f'(c) > 0.
APPEARS IN
RELATED QUESTIONS
Find the intervals in which the function f(x) = 3x4 − 4x3 − 12x2 + 5 is
(a) strictly increasing
(b) strictly decreasing
Find the intervals in which the function f given by f(x) = 2x2 − 3x is
- strictly increasing
- strictly decreasing
Prove that f(x) = ax + b, where a, b are constants and a < 0 is a decreasing function on R ?
Find the interval in which the following function are increasing or decreasing f(x) = x4 − 4x3 + 4x2 + 15 ?
Show that the function f(x) = sin (2x + π/4) is decreasing on (3π/8, 5π/8) ?
Show that the function x2 − x + 1 is neither increasing nor decreasing on (0, 1) ?
Show that f(x) = x2 − x sin x is an increasing function on (0, π/2) ?
Find 'a' for which f(x) = a (x + sin x) + a is increasing on R ?
Write the set of values of a for which the function f(x) = ax + b is decreasing for all x ∈ R ?
The function \[f\left( x \right) = \log_e \left( x^3 + \sqrt{x^6 + 1} \right)\] is of the following types:
The function f(x) = −x/2 + sin x defined on [−π/3, π/3] is
If x = cos2 θ and y = cot θ then find `dy/dx at θ=pi/4`
Find `dy/dx,if e^x+e^y=e^(x-y)`
If the demand function is D = 50 - 3p - p2, find the elasticity of demand at (a) p = 5 (b) p = 2 , Interpret your result.
Show that function f(x) =`("x - 2")/("x + 1")`, x ≠ -1 is increasing.
A man of height 1.9 m walks directly away from a lamp of height 4.75m on a level road at 6m/s. The rate at which the length of his shadow is increasing is
Let f(x) = x3 + 9x2 + 33x + 13, then f(x) is ______.
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
The function f (x) = 2 – 3 x is ____________.
The function f(x) = tan-1 x is ____________.
If f(x) = sin x – cos x, then interval in which function is decreasing in 0 ≤ x ≤ 2 π, is:
Find the interval in which the function `f` is given by `f(x) = 2x^2 - 3x` is strictly decreasing.
The interval in which `y = x^2e^(-x)` is increasing with respect to `x` is
y = log x satisfies for x > 1, the inequality ______.
The intevral in which the function f(x) = 5 + 36x – 3x2 increases will be ______.
Find the values of x for which the function f(x) = `x/(x^2 + 1)` is strictly decreasing.
For \[f'(x)=12(x-3)(x+2)\], what is the nature of \[f\] on \[(-2,3)\]?
