Question

 If$\ f(x) = 3x^2 – 2x + 5$ , find f[1, 2], f[2, 3] and f[1, 2, 3].

Answer 1

The function $f(x)=3x^2-2x+5$ is continuous for $x\in \R$ as polynomial.

$$f'(x)=6x-2$$

$$f'(x)=0=>6x-2=0=>x=\dfrac{1}{3}$$

If $x>\dfrac{1}{3}, f'(x)>0, f(x)$ is strictly increasing.

$$f(1)=3(1)^2-2(1)+5=6$$

$$f(2)=3(2)^2-2(2)+5=13$$

$$f(3)=3(3)^2-2(3)+5=26$$

$$f:[1,2]\to[6,26]$$

$$f:[2,3]\to[13,26]$$

$$f:\{1,2,3\}\to\{6, 13,26\}$$