Answer to Question #216461 in Calculus for ABUSALMA

Question #216461

1)                 If f(x) = 3x2 – 2x + 5, find f[1, 2], f[2, 3] and f[1, 2, 3].


1
Expert's answer
2021-07-21T15:01:05-0400

(1.) The function f(x)=3x22x+5f(x)=3x^2-2x+5 is continuous for all xRx\in \R as polynomial.

and the first derivative of this function f(x) is



f(x)=6x2f'(x)=6x-2f(x)=0    6x2=0    x=13f'(x)=0\implies 6x-2=0\implies x=\dfrac{1}{3}

If x>13,f(x)>0,f(x)x>\dfrac{1}{3}, f'(x)>0, f(x) is strictly increasing.




f(1)=3(1)22(1)+5=6f(1)=3(1)^2-2(1)+5=6f(2)=3(2)22(2)+5=13f(2)=3(2)^2-2(2)+5=13f(3)=3(3)22(3)+5=26f(3)=3(3)^2-2(3)+5=26    f:[1,2][6,13]\implies f:[1,2]\to[6,13]    f:[2,3][13,26]\implies f:[2,3]\to[13,26]    f:{1,2,3}{6,13,26}\implies f:\{1,2,3\}\to\{6, 13,26\}

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