The maximum value of 5+20x-4x2, when x is a real number is
Answers
Answered by
22
f(x) = 5 + 20x - 4x²
a = -4
b = 20
c = 5
y max
= (b² - 4ac)/(-4a)
= [20² - 4 . (-4) . 5]/[-4 . (-4)]
= (400 + 80)/16
= 480/16
= 30
a = -4
b = 20
c = 5
y max
= (b² - 4ac)/(-4a)
= [20² - 4 . (-4) . 5]/[-4 . (-4)]
= (400 + 80)/16
= 480/16
= 30
Answered by
16
Solution :-
To find the value of x, coordinate we use :
x = - b/2*a where, a = - 4 and b = 20
So,
x = (- 20)/2*(- 4)
x = - 20/(- 8)
x = 20/8
x = 5/2
Now, to find the value of y coordinate, we will substitute the x = 5/2 in the given equation.
⇒ - 4x² + 20 + 5
⇒ y = (- 4)*(5/2)² + 20*(5/2) + 5
⇒ (- 4)/(25/4) + 100/2 + 5
⇒ - 25 + 50 + 5
⇒ 55 - 25
⇒ y = 30
This is the value of y coordinate of the vertex (maximum).
Answer
To find the value of x, coordinate we use :
x = - b/2*a where, a = - 4 and b = 20
So,
x = (- 20)/2*(- 4)
x = - 20/(- 8)
x = 20/8
x = 5/2
Now, to find the value of y coordinate, we will substitute the x = 5/2 in the given equation.
⇒ - 4x² + 20 + 5
⇒ y = (- 4)*(5/2)² + 20*(5/2) + 5
⇒ (- 4)/(25/4) + 100/2 + 5
⇒ - 25 + 50 + 5
⇒ 55 - 25
⇒ y = 30
This is the value of y coordinate of the vertex (maximum).
Answer
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