Find the greatest value of 3+5x-2x2 for all real values of x
Answers
Answered by
6
Hey
The given equation is :-
3 + 5x - 2x²
Or we can write
-2x² + 5x + 3
It is a quadratic equation , so only two value if x will come .
Let's find out :-
- 2 x² + 5x + 3 = 0
=> 2x² - 5x - 3 = 0
=> 2x² - 6x + x - 3 = 0
=> 2x ( x - 3 ) + 1 ( x - 3 ) = 0
=> ( 2x + 1 ) ( x - 3 ) = 0
Now ,
2x + 1 = 0
=> x = -1 / 2
And
x - 3 = 0
=> x = 3
So ,
greatest value of x = 3
thanks :)
The given equation is :-
3 + 5x - 2x²
Or we can write
-2x² + 5x + 3
It is a quadratic equation , so only two value if x will come .
Let's find out :-
- 2 x² + 5x + 3 = 0
=> 2x² - 5x - 3 = 0
=> 2x² - 6x + x - 3 = 0
=> 2x ( x - 3 ) + 1 ( x - 3 ) = 0
=> ( 2x + 1 ) ( x - 3 ) = 0
Now ,
2x + 1 = 0
=> x = -1 / 2
And
x - 3 = 0
=> x = 3
So ,
greatest value of x = 3
thanks :)
Answered by
6
Answer:
Step-by-step explanation:
Find the maximum or minimum value of f(x) = 2x^2 + 3x - 5
f(x) = 2x^2 + 3x -5
First we notice that the function has a positive coefficient for x^2.
Then the fucntion has a minimum values.
Now we will find the derivatives zero.
==> f'(x) = 4x +3 = 0
==> 4x = -3
==> x = -3/4
==> f(-3/4)= 2(-3/4)^2 + 3(-3/4) -5
= 2* 9/16 - 9/4 - 5
= (18- 36 - 80)/16 = -98/16 = -49/8.
==> The minimum values is f(-3/4) = -49/8.
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