English

Choose the correct alternative: The function f(x) = x3 – 3x2 + 3x – 100, x ∈ R is

Advertisements
Advertisements

Question

Choose the correct alternative:

The function f(x) = x3 – 3x2 + 3x – 100, x ∈ R is

Options

  • increasing for all x ∈ R, x ≠ 1 

  • decreasing

  • neither increasing nor decreasing

  • decreasing for all x ∈ R, x ≠ 1

MCQ
Advertisements

Solution

increasing for all x ∈ R, x ≠ 1 

shaalaa.com
  Is there an error in this question or solution?
Chapter 1.4: Applications of Derivatives - Q.1

RELATED QUESTIONS

Test whether the function is increasing or decreasing. 

f(x) = `"x" -1/"x"`, x ∈ R, x ≠ 0, 


Show that the function given by f(x) = 3x + 17 is strictly increasing on R.


On which of the following intervals is the function f given byf(x) = x100 + sin x –1 strictly decreasing?


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)`


Find the intervals in which the function f given by `f(x) = (4sin x - 2x - x cos x)/(2 + cos x)` is (i) increasing (ii) decreasing.


Find the interval in which the following function are increasing or decreasing  f(x) = 5x3 − 15x2 − 120x + 3 ?


Find the interval in which the following function are increasing or decreasing \[f\left( x \right) = \frac{3}{2} x^4 - 4 x^3 - 45 x^2 + 51\] ?


Show that f(x) = loga x, 0 < a < 1 is a decreasing function for all x > 0 ?


Show that f(x) = tan−1 (sin x + cos x) is a decreasing function on the interval (π/4, π/2) ?


State when a function f(x) is said to be increasing on an interval [a, b]. Test whether the function f(x) = x2 − 6x + 3 is increasing on the interval [4, 6] ?


Find the intervals in which f(x) = (x + 2) e−x is increasing or decreasing ?


Let f defined on [0, 1] be twice differentiable such that | f (x) | ≤ 1 for all x ∈ [0, 1]. If f(0) = f(1), then show that | f'(x) | < 1 for all x ∈ [ 0, 1] ?


What are the values of 'a' for which f(x) = ax is decreasing on R ? 


Find 'a' for which f(x) = a (x + sin x) + a is increasing on R ?


If g (x) is a decreasing function on R and f(x) = tan−1 [g (x)]. State whether f(x) is increasing or decreasing on R ?


The function \[f\left( x \right) = \log_e \left( x^3 + \sqrt{x^6 + 1} \right)\] is of the following types:


The radius r of a right circular cylinder is increasing uniformly at the rate of 0·3 cm/s and its height h is decreasing at the rate of 0·4 cm/s. When r = 3·5 cm and h = 7 cm, find the rate of change of the curved surface area of the cylinder. \[\left[ \text{ Use } \pi = \frac{22}{7} \right]\]


Prove that the function f : N → N, defined by f(x) = x2 + x + 1 is one-one but not onto. Find the inverse of f: N → S, where S is range of f.


Test whether the following functions are increasing or decreasing: f(x) = `x-(1)/x`, x ∈ R, x ≠ 0.


The price P for the demand D is given as P = 183 + 120D − 3D2, then the value of D for which price is increasing, is ______.


The area of the square increases at the rate of 0.5 cm2/sec. The rate at which its perimeter is increasing when the side of the square is 10 cm long is ______.


The function f(x) = x3 - 3x is ______.


For every value of x, the function f(x) = `1/7^x` is ______ 


Show that f(x) = 2x + cot–1x + `log(sqrt(1 + x^2) - x)` is increasing in R


Let f be a real valued function defined on (0, 1) ∪ (2, 4) such that f '(x) = 0 for every x, then ____________.


If f(x) = sin x – cos x, then interval in which function is decreasing in 0 ≤ x ≤ 2 π, is:


The function `"f"("x") = "x"/"logx"` increases on the interval


The interval in which `y = x^2e^(-x)` is increasing with respect to `x` is


Find the interval in which the function f(x) = x2e–x is strictly increasing or decreasing.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×