Advertisements
Advertisements
प्रश्न
Prove that the function f(x) = tanx – 4x is strictly decreasing on `((-pi)/3, pi/3)`
उत्तर
f(x) = tan x – 4x
⇒ f'(x) = sec2x – 4
When `(-pi)/4 < x < pi/3, 1 < secx < 2`
Therefore, 1 < sec2x < 4
⇒ 3 < (sec2x – 4) < 0
Thus for `(-pi)/4 < x < pi/3`, f'(x) < 0
Hence f is strictly decreasing on `((-pi)/3, pi/3)`.
APPEARS IN
संबंधित प्रश्न
Prove that the function f given by f(x) = log sin x is strictly increasing on `(0, pi/2)` and strictly decreasing on `(pi/2, pi)`
Prove that the function f given by f(x) = log cos x is strictly decreasing on `(0, pi/2)` and strictly increasing on `((3pi)/2, 2pi).`
Show that f(x) = \[\frac{1}{1 + x^2}\] is neither increasing nor decreasing on R ?
Find the interval in which the following function are increasing or decreasing f(x) = −2x3 − 9x2 − 12x + 1 ?
Find the interval in which the following function are increasing or decreasing f(x) = (x − 1) (x − 2)2 ?
Show that f(x) = x2 − x sin x is an increasing function on (0, π/2) ?
Find the values of b for which the function f(x) = sin x − bx + c is a decreasing function on R ?
Function f(x) = cos x − 2 λ x is monotonic decreasing when
Function f(x) = x3 − 27x + 5 is monotonically increasing when
In the interval (1, 2), function f(x) = 2 | x − 1 | + 3 | x − 2 | is
Using truth table show that ∼ (p → ∼ q) ≡ p ∧ q
The edge of a cube is decreasing at the rate of`( 0.6"cm")/sec`. Find the rate at which its volume is decreasing, when the edge of the cube is 2 cm.
Find the values of x for which the following functions are strictly decreasing : f(x) = `x + (25)/x`
Test whether the following function is increasing or decreasing.
f(x) = `7/"x" - 3`, x ∈ R, x ≠ 0
Choose the correct alternative.
The function f(x) = x3 - 3x2 + 3x - 100, x ∈ R is
Prove that function f(x) = `x - 1/x`, x ∈ R and x ≠ 0 is increasing function
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 values of k for which the function f(x) = kx3 – 6x2 + 12x + 11 may be increasing on R are ______.
If f(x) = x3 – 15x2 + 84x – 17, then ______.
The function f(x) = x2 – 2x is increasing in the interval ____________.
In `(0, pi/2),` the function f (x) = `"x"/"sin x"` is ____________.
If f(x) = sin x – cos x, then interval in which function is decreasing in 0 ≤ x ≤ 2 π, is:
The interval in which `y = x^2e^(-x)` is increasing with respect to `x` is
Show that function f(x) = tan x is increasing in `(0, π/2)`.
The function f(x) = tan–1(sin x + cos x) is an increasing function in ______.
Read the following passage:
|
The use of electric vehicles will curb air pollution in the long run. V(t) = `1/5 t^3 - 5/2 t^2 + 25t - 2` where t represents the time and t = 1, 2, 3, ...... corresponds to years 2001, 2002, 2003, ...... respectively. |
Based on the above information, answer the following questions:
- Can the above function be used to estimate number of vehicles in the year 2000? Justify. (2)
- Prove that the function V(t) is an increasing function. (2)
The function f(x) = x3 + 3x is increasing in interval ______.
