Determine whether a function increases or decreases using its derivative - High school Calculus Exercises

Let f be the function defined as follows:

f:x\longmapsto 2x^2-4x

Determine whether f is increasing or decreasing between 1 and 5.

f is decreasing on \left[1{,}5\right].

f is increasing on \left[1{,}5\right].

f is not monotonic on \left[1{,}5\right].

Let f be the function defined as follows:

f:x\longmapsto x^{3}-4x^{2}+5x-7

Determine whether f is increasing or decreasing.

f is increasing when x\in\left(-\infty,1\right)\cup\left(\dfrac{5}{3},\infty\right) and decreasing when x\in\left(1,\dfrac{5}{3}\right).

f is increasing when x\in\mathbb{R}.

f is increasing when x\in\left(-\infty,-1\right) and decreasing when x\in\left(-1,\infty\right).

f is increasing when x\in\left(-\infty,-\dfrac{3}{5}\right)\cup\left(\dfrac{1}{2},\infty\right) and decreasing when x\in\left(-\dfrac{3}{5},\dfrac{1}{2}\right).

Let f be the function defined as follows:

f:x\longmapsto x^{2}\ln\left(x\right)

Determine whether f is increasing or decreasing on \left(0,\infty\right).

f is decreasing when x\in\left(0,e^{2}\right) and increasing when x\in\left(e^{2},\infty\right).

f is decreasing when x\in\left(0,\dfrac{1}{e^{2}}\right) and increasing when x\in\left(\dfrac{1}{e^{2}},\infty\right).

f is decreasing when x\in\left(0,\dfrac{\sqrt{e}}{e}\right) and increasing when x\in\left(\dfrac{\sqrt{e}}{e},\infty\right).

f is decreasing when x\in\left(0,\dfrac{1}{e^{2}}\right)\cup\left(e,\infty\right) and increasing when x\in\left(\dfrac{1}{e^{2}},e\right).

Let f be the function defined as follows:

f:x\longmapsto \dfrac{x^{2}}{x-1}

Determine whether f is increasing or decreasing on \left(-\infty,1\right)\cup\left(1,\infty\right).

f is increasing when x\in\left(0{,}1\right)\cup\left(1{,}2\right) and decreasing when x\in\left(-\infty,0\right)\cup\left(2,\infty\right).

f is increasing when x\in\left(-1{,}1\right)\cup\left(1{,}2\right) and decreasing when x\in\left(-\infty,-1\right)\cup\left(2,\infty\right).

f is decreasing when x\in\left(0{,}1\right)\cup\left(1{,}2\right) and increasing when x\in\left(-\infty,0\right)\cup\left(2,\infty\right).

f is decreasing when x\in\left(-1{,}1\right)\cup\left(1{,}2\right) and increasing when x\in\left(-\infty,-1\right)\cup\left(2,\infty\right).

Let f be the function defined as follows:

f:x\longmapsto x^{4}e^{2x}

Determine whether f is increasing or decreasing.

f is increasing when x\in\left(-\infty,-2\right)\cup\left(0,\infty\right) and decreasing when x\in\left(-2{,}0\right).

f is decreasing when x\in\left(-\infty,2\right) and increasing when x\in\left(2,\infty\right).

f is increasing when x\in\left(0,\infty\right) and decreasing when x\in\left(-\infty,0\right).

f is increasing when x\in\left(-\infty,2\right)\cup\left(6,\infty\right) and decreasing when x\in\left(2{,}6\right).

Let f be the function defined as follows:

f:x\longmapsto \sqrt{x^{2}+4x+5}

Determine whether f is increasing or decreasing.

f is decreasing when x\in\left(-\infty,2\right) and increasing when x\in\left(2,\infty\right).

f is decreasing when x\in\left(-\infty,-4\right) and increasing when x\in\left(-4,\infty\right).

f is decreasing when x\in\left(-\infty,-2\right) and increasing when x\in\left(-2,\infty\right).

f is decreasing when x\in\left(-\infty,4\right) and increasing when x\in\left(4,\infty\right).

Let f be the function defined as follows:

f:x\longmapsto \dfrac{x+3}{2x-4}

Determine whether f is increasing or decreasing on \left(-\infty,2\right)\cup\left(2,\infty\right).

f is decreasing when x\in\left(-\infty,2\right)\cup\left(2,\infty\right).

f is increasing when x\in\left(-\infty,2\right)\cup\left(2,\infty\right).

f is decreasing when x\in\left(-\infty,2\right) and increasing when x\in\left(2,\infty\right).

f is increasing when x\in\left(-\infty,2\right) and decreasing when x\in\left(2,\infty\right).