Determine whether a function is convex or concave using the second-order derivative - High school Calculus Exercises

Are the following functions convex or concave?

f:x\longmapsto 2x^2-4x+5

f is concave on \left[-\infty,1\right] and convex on \left[1,\infty\right).

f is convex on \left[-\infty,1\right] and concave on \left[1,\infty\right).

f is concave on \mathbb{R}.

f is convex on \mathbb{R}.

f:x\longmapsto x^{3}+6x^{2}-7x-2

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

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

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

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

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

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

f is concave when x\in\left(-2-\sqrt{2},-2+\sqrt{2}\right) and convex when x\in\left(-\infty,-2-\sqrt{2}\right)\cup\left(-2+\sqrt{2},\infty\right).

f is convex when x\in\left(-2-2\sqrt{2},-2+2\sqrt{2}\right) and concave when x\in\left(-\infty,-2-2\sqrt{2}\right)\cup\left(-2+2\sqrt{2},\infty\right).

f is concave when x\in\left(-2-2\sqrt{2},-2+2\sqrt{2}\right) and convex when x\in\left(-\infty,-2-2\sqrt{2}\right)\cup\left(-2+2\sqrt{2},\infty\right).

f:x\longmapsto x\ln\left(x\right), x\in\left(0,\infty\right)

f is convex when x\in\left(0,e\right) and concave when x\in\left(e,\infty\right).

f is concave when x\in\left(0,e\right) and convex when x\in\left(e,\infty\right).

f is concave when x\in\left(0,\infty\right).

f is convex when x\in\left(0,\infty\right).

f:x\longmapsto \dfrac{x-1}{x+1}, x\in\left(-\infty,-1\right)\cup\left(-1,\infty\right)

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

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

f is concave when x\in\left(-\infty,-1\right)\cup\left(-1,\infty\right).

f is convex when x\in\left(-\infty,-1\right)\cup\left(-1,\infty\right).

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

f is convex when x\in\left(-\infty,-\dfrac{\sqrt{2}}{2}\right)\cup\left(\dfrac{\sqrt{2}}{2},\infty\right) and concave when x\in\left(-\dfrac{\sqrt{2}}{2},\dfrac{\sqrt{2}}{2}\right).

f is convex when x\in\left(-\infty,-\dfrac{\sqrt{2}}{4}\right)\cup\left(\dfrac{\sqrt{2}}{4},\infty\right) and concave when x\in\left(-\dfrac{\sqrt{2}}{4},\dfrac{\sqrt{2}}{4}\right).

f is concave when x\in\left(-\infty,-3\right)\cup\left(3,\infty\right) and convex when x\in\left(-3{,}3\right).

f is convex when x\in\left(-\infty,-\dfrac{\sqrt{3}}{2}\right)\cup\left(\dfrac{\sqrt{3}}{2},\infty\right) and concave when x\in\left(-\dfrac{\sqrt{3}}{2},\dfrac{\sqrt{3}}{2}\right).

f:x\longmapsto x^{2}\sqrt{x}, x\in\left[0,\infty\right)

f is concave when x\in\left[0,\infty\right).

f is convex when x\in\left[0,\infty\right).

f is concave when x\in\left[0{,}1\right) and convex when x\in\left(1,\infty\right).

f is convex when x\in\left[0{,}1\right) and concave when x\in\left(1,\infty\right).