Advertisements
Advertisements
Question
Show that the function f given by f(x) = 10x is increasing for all x ?
Advertisements
Solution
\[f\left( x \right) = {10}^x \]
\[f'\left( x \right) = {10}^x \log 10 > 0, \forall x \in R\]
\[\text { So, f(x) is increasing for all x } \in R .\]
APPEARS IN
RELATED QUESTIONS
Find the value(s) of x for which y = [x(x − 2)]2 is an increasing function.
Find the value of c in Rolle's theorem for the function `f(x) = x^3 - 3x " in " (-sqrt3, 0)`
Prove that the logarithmic function is strictly increasing on (0, ∞).
Find the intervals in which the function f given by `f(x) = x^3 + 1/x^3 x != 0`, is (i) increasing (ii) decreasing.
Let f be a function defined on [a, b] such that f '(x) > 0, for all x ∈ (a, b). Then prove that f is an increasing function on (a, b).
Show that f(x) = \[\frac{1}{1 + x^2}\] decreases in the interval [0, ∞) and increases in the interval (−∞, 0] ?
Find the interval in which the following function are increasing or decreasing f(x) = 2x3 − 15x2 + 36x + 1 ?
Find the interval in which the following function are increasing or decreasing f(x) = −2x3 − 9x2 − 12x + 1 ?
Show that the function f(x) = sin (2x + π/4) is decreasing on (3π/8, 5π/8) ?
Show that f(x) = x9 + 4x7 + 11 is an increasing function for all x ∈ R ?
Prove that the following function is increasing on R f \[(x) =\]3 \[x^5\] + 40 \[x^3\] + 240\[x\] ?
If the function f(x) = 2x2 − kx + 5 is increasing on [1, 2], then k lies in the interval
In the interval (1, 2), function f(x) = 2 | x − 1 | + 3 | x − 2 | is
Function f(x) = 2x3 − 9x2 + 12x + 29 is monotonically decreasing when
Function f(x) = loga x is increasing on R, if
The price P for demand D is given as P = 183 + 120 D – 3D2.
Find D for which the price is increasing.
Test whether the following functions are increasing or decreasing: f(x) = `x-(1)/x`, x ∈ R, x ≠ 0.
Find the values of x for which the function f(x) = x3 – 12x2 – 144x + 13 (a) increasing (b) decreasing
Show that y = `log (1 + x) – (2x)/(2 + x), x > - 1` is an increasing function on its domain.
Solve the following : Find the intervals on which the function y = xx, (x > 0) is increasing and decreasing.
Solve the following:
Find the intervals on which the function f(x) = `x/logx` is increasing and decreasing.
Find the values of x for which the function f(x) = x3 – 6x2 – 36x + 7 is strictly increasing
Find the values of x for which f(x) = 2x3 – 15x2 – 144x – 7 is
- Strictly increasing
- strictly decreasing
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 ______
Let f(x) = x3 + 9x2 + 33x + 13, then f(x) is ______.
For every value of x, the function f(x) = `1/7^x` is ______
Determine for which values of x, the function y = `x^4 – (4x^3)/3` is increasing and for which values, it is decreasing.
Show that for a ≥ 1, f(x) = `sqrt(3)` sinx – cosx – 2ax + b ∈ is decreasing in R
The values of a for which the function f(x) = sinx – ax + b increases on R are ______.
The function f (x) = 2 – 3 x is ____________.
The function f (x) = x2, for all real x, is ____________.
The function f(x) = tan-1 x is ____________.
Let f (x) = tan x – 4x, then in the interval `[- pi/3, pi/3], "f"("x")` is ____________.
The length of the longest interval, in which the function `3 "sin x" - 4 "sin"^3"x"` is increasing, is ____________.
Find the interval in which the function `f` is given by `f(x) = 2x^2 - 3x` is strictly decreasing.
Let f(x) be a function such that; f'(x) = log1/3(log3(sinx + a)) (where a ∈ R). If f(x) is decreasing for all real values of x then the exhaustive solution set of a is ______.
If f(x) = x + cosx – a then ______.
In which one of the following intervals is the function f(x) = x3 – 12x increasing?
The function f(x) = xex(1 − x), x ∈ R, is ______.
