12. Find the greatest or least value of
X + 2/2x2 + 3x + 6 ifx belong to R
Answers
Answered by
3
Answer:
Consider the given function.
f(x)=
2x
2
+3x+6
x+2
Clearly, the function (2x
2
+3x+6) is a quadratic function with a=2>0 and so it will have its minimum value at x=−
2a
b
=−
4
3
and the minimum value will be,
2(−
4
3
)
2
+3(−
4
3
)+6=
8
9
−
4
9
+6=
8
9−18+48
=
8
39
We can see that,
D<0 and 2x
2
+3x+6>0 ∀ x
Hence,
0<
(2x
2
+3x+6)
1
<
39
8
∀x∈R
Therefore, f(x) will have its maximum value at x=−
4
3
and its value will be,
(
8
39
)
(−
4
3
)+2
=
39×4
5×8
=
39
10
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