Advertisements
Advertisements
Question
Find the intervals in which the function f given by f(x) = 2x2 − 3x is
- strictly increasing
- strictly decreasing
Advertisements
Solution
f(x) = 2x2 - 3x
f'(x) = 4x - 3
If f'(x) = 0
4x - 3 = 0
x = `3/4`
(a) f'(x) = 4x - 3 > 0, x `in (3/4, infty)`
Therefore, the function is continuously increasing in `(3/4, infty)`.
(b) f'(x) = cos x < 0, x `in (- infty, 3/4)`
Therefore, the function is continuously decreasing in `(- infty, 3/4)`.
APPEARS IN
RELATED QUESTIONS
Find the intervals in which the function f(x) = 3x4 − 4x3 − 12x2 + 5 is
(a) strictly increasing
(b) strictly decreasing
Test whether the function is increasing or decreasing.
f(x) = `"x" -1/"x"`, x ∈ R, x ≠ 0,
Find the intervals in which the function f given by f(x) = 2x3 − 3x2 − 36x + 7 is
- Strictly increasing
- Strictly decreasing
Find the intervals in which the following functions are strictly increasing or decreasing:
6 − 9x − x2
Prove that the function f(x) = loge x is increasing on (0, ∞) ?
Find the interval in which the following function are increasing or decreasing f(x) = x2 + 2x − 5 ?
Find the interval in which the following function are increasing or decreasing f(x) = 6 − 9x − x2 ?
Find the interval in which the following function are increasing or decreasing f(x) = x3 − 6x2 − 36x + 2 ?
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 ?
Show that f(x) = e2x is increasing on R.
Show that f(x) = (x − 1) ex + 1 is an increasing function for all x > 0 ?
Prove that the function f(x) = x3 − 6x2 + 12x − 18 is increasing on R ?
Show that f(x) = tan−1 x − x is a decreasing function on R ?
Find the intervals in which f(x) = log (1 + x) −\[\frac{x}{1 + x}\] is increasing or decreasing ?
What are the values of 'a' for which f(x) = ax is decreasing on R ?
Find the values of 'a' for which the function f(x) = sin x − ax + 4 is increasing function on R ?
Find the intervals in which the function \[f(x) = \frac{3}{2} x^4 - 4 x^3 - 45 x^2 + 51\] is
(a) strictly increasing
(b) strictly decreasing
Using truth table show that ∼ (p → ∼ q) ≡ p ∧ q
If the demand function is D = 50 - 3p - p2, find the elasticity of demand at (a) p = 5 (b) p = 2 , Interpret your result.
Find the values of x for which the following functions are strictly increasing:
f(x) = 3 + 3x – 3x2 + x3
Find the values of x for which the following func- tions are strictly increasing : f(x) = x3 – 6x2 – 36x + 7
Find the values of x for which the following functions are strictly decreasing : f(x) = `x + (25)/x`
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 increasing function.
f(x) = x2 + 2x - 5
Find the value of x, such that f(x) is decreasing function.
f(x) = 2x3 - 15x2 - 144x - 7
The total cost function for production of articles is given as C = 100 + 600x – 3x2, then the values of x for which the total cost is decreasing is ______
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 ______
For every value of x, the function f(x) = `1/7^x` is ______
If f(x) = `x^(3/2) (3x - 10)`, x ≥ 0, then f(x) is increasing in ______.
The function f(x) = tanx – x ______.
The function f(x) = `(2x^2 - 1)/x^4`, x > 0, decreases in the interval ______.
The function f: N → N, where
f(n) = `{{:(1/2(n + 1), "If n is sold"),(1/2n, "if n is even"):}` is
Let x0 be a point in the domain of definition of a real valued function `f` and there exists an open interval I = (x0 – h, ro + h) containing x0. Then which of the following statement is/ are true for the above statement.
Function given by f(x) = sin x is strictly increasing in.
Show that function f(x) = tan x is increasing in `(0, π/2)`.
If f(x) = `x - 1/x`, x∈R, x ≠ 0 then f(x) is increasing.
