Monotonicity of a Function about a Point

Q.

A function f(x) is defined on [a, b]. What should be the condition for the function to be a strictly decreasing function at x = b ?

1. $f\left(b\right)>f(b-h)$

2. $f(b-h)>f\left(b\right)$

3. $f\left(b\right)\ge f(b-h)$

4. $f(b-h)\ge f\left(b\right)$

Q.

A function f(x) is called as a strictly increasing function about a point ‘a’ If -

Where 'h' is a positive real number tending to zero.

1. f(a-h) ≥ f(a) ≥ f(a+h)

2. f(a+h) > f(a) > f(a - h)

3. f(a-h) > f(a) > f(a+ h)

4. f(a+h) ≥ f(a) ≥ f (a-h)

Q. the whole sqrt x-sqrt x^2-1 find domain

Q.

Monotonicity of a function at a point is discussed only in the neighborhood of the point.

1. True

2. False

Q. Find the area of the region bounded by the following hyperboles using integration: y²-ax=a² y²+ax=a²

Q.

A function f(x) is called as a strictly increasing function about a point ‘a’ If -

Where 'h' is a positive real number tending to zero.

1. $f(a+h)>f\left(a\right)>f(a-h)$

2. $f(a-h)>f\left(a\right)>f(a+h)$

3. $f(a+h)\ge f\left(a\right)\ge f(a-h)$

4. $f(a-h)\ge f\left(a\right)\ge f(a+h)$

Q. What is domain and range of the function whose expression is given under odd root ³√, ⁵√ etc

Q. For the function $f\left(x\right)=\left[x\right]-\left\{x\right\}$ , which of the following is true regarding its monotonicity at $x=\frac{1}{2}?$
$\left(\right[\cdot ]\text{denotes the greatest integer function and}\{\cdot \}\text{denotes fractional part of}x)$

Q.

A function f(x) is defined on [a, b]. What should be the condition for the function to be a strictly decreasing function at x = b ?

1. $f\left(b\right)>f(b-h)$

2. $f(b-h)>f\left(b\right)$

3. $f\left(b\right)\ge f(b-h)$

4. $f(b-h)\ge f\left(b\right)$

Q. Find domain and range of the function:f(x)=x^2+3

Q.

A function f(x) is defined on [a, b]. What should be the condition for the function to be a strictly decreasing function at x = b ?

1. $f\left(b\right)>f(b-h)$

2. $f(b-h)>f\left(b\right)$

3. $f\left(b\right)\ge f(b-h)$

4. $f(b-h)\ge f\left(b\right)$

Q.

A function f(x) is called as a strictly increasing function about a point ‘a’ If -

Where 'h' is a positive real number tending to zero.

1. $f(a+h)>f\left(a\right)>f(a-h)$

2. $f(a-h)>f\left(a\right)>f(a+h)$

3. $f(a+h)\ge f\left(a\right)\ge f(a-h)$

4. $f(a-h)\ge f\left(a\right)\ge f(a+h)$

Q.

Monotonicity of a function at a point is discussed only in the neighborhood of the point.

1. True

2. False

Q.

A function f(x) is called as a strictly increasing function about a point ‘a’ If -

Where 'h' is a positive real number tending to zero.

1. f(a-h) > f(a) > f(a+ h)

2. f(a+h) > f(a) > f(a - h)

3. f(a+h) ≥ f(a) ≥ f (a-h)

4. f(a-h) ≥ f(a) ≥ f(a+h)

Q.

Monotonicity of a function at a point is discussed only in the neighborhood of the point.

1. True

2. False

Q.

A function f(x) is defined on [a, b]. What should be the condition for the function to be a strictly decreasing function at x = b ?

1. f(b) > f(b - h)

2. f(b-h) ≥ f(b)

3. f(b-h) > f(b)

4. f(b) ≥ f (b-h)

Q.

A function f(x) is called as a strictly increasing function about a point ‘a’ If -

Where 'h' is a positive real number tending to zero.

1. $f(a+h)>f\left(a\right)>f(a-h)$

2. $f(a-h)>f\left(a\right)>f(a+h)$

3. $f(a+h)\ge f\left(a\right)\ge f(a-h)$

4. $f(a-h)\ge f\left(a\right)\ge f(a+h)$