Question

Tìm giá trị lớn nhất của biểu thức:

a) C = 20013 - \(\left|5-2x\right|\)

b) D = 7 - \(\left|\dfrac{2}{3}+\dfrac{1}{4}x\right|\)

c) N = 1 + \(\dfrac{1}{\left|2x-1\right|}\)

d) E = 13 - ( 2x - \(\dfrac{1}{3}\) )²

e) F = -( 3x + \(\dfrac{1}{2}\) )⁴ + 2015

g) G = \(\dfrac{2x^2+15}{x^2+3}\)

Answer 1

a) C = 20013 - $\left|5-2x\right|$

$do\; \backslash (-\backslash left|5-2x\backslash right|\backslash le0\backslash forall\; x\backslash )$

=> 20013-\(\left|5-2x\right|\le20013\)

=>A≤20013

=> GTLN C =20013 khi 5-2x=0

=> 2x=5

=> x=\(\dfrac{5}{2}\)

vậy GTLN C = 20013 khi x=\(\dfrac{5}{2}\)

b) D = 7 - \(\left|\dfrac{2}{3}+\dfrac{1}{4}x\right|\)

do \(-\left|\dfrac{2}{3}+\dfrac{1}{4}x\right|\le0\forall x\)

=> 7-\(\left|\dfrac{2}{3}+\dfrac{1}{4}x\right|\le7\)

=> D≤7

=> GTLN D =7 khi \(\dfrac{2}{3}+\dfrac{1}{4}x=0\)

=> x=-\(\dfrac{8}{3}\)