find the maxima and minima value this equation x^4 -8x^3 +22x^2 -24x
Answers
Answer:
Step-by-step explanation:
easy
f(x) = x³ - 2x² + x + 6
Find the first derivative:
f(x) = x^4-8x³ + 22x² -24x
f'(x) =4 x^3-24 x^2+44 x-24
f'(x) = (x - 1)(x - 3)
(x -1) (x - 3) = 0
x = 1 or x = 3
Find the second derivative:
f'(x) = 4 x^3-24 x^2+44 x-24
f''(x) = 12x^2-48x+44
Find max / min point:
When x = 1
f''(x) =12*1^2-48*1+44
f''(x) = 8 > 0 minimum point
When x = 3
f''(x) = 12*3^2-48*3+44
f''(x) = 8 > 0
same points
Find minimum point:
When x = 8,
f(x) = x^4 -8x^3 +22x^2 -24x
f(x) = 8^4-8*8^3+22*8^2-24*8
⇒ minimum point = 1216
Find the maximum point:
when x = 3
f(x) = 8^4-8*8^3+22*8^2-24*8
f(x) =1216
maxima and minima =1216
Answer:
f(x) = x³ - 2x² + x + 6
Find the first derivative:
f(x) = x^4-8x³ + 22x² -24x
f'(x) =4 x^3-24 x^2+44 x-24
f'(x) = (x - 1)(x - 3)
(x -1) (x - 3) = 0
x = 1 or x = 3
Find the second derivative:
f'(x) = 4 x^3-24 x^2+44 x-24
f''(x) = 12x^2-48x+44
Find max / min point:
When x = 1
f''(x) =12*1^2-48*1+44
f''(x) = 8 > 0 minimum point
When x = 3
f''(x) = 12*3^2-48*3+44
f''(x) = 8 > 0
same points
Find minimum point:
When x = 8,
f(x) = x^4 -8x^3 +22x^2 -24x
f(x) = 8^4-8*8^3+22*8^2-24*8
⇒ minimum point = 1216
Find the maximum point:
when x = 3
f(x) = 8^4-8*8^3+22*8^2-24*8
f(x) =1216
maxima and minima =1216
Step bro ω≥