Question

Q.2) The greatest and the least value of f(x)=x^4-8x^3+22x^2-24x+1 in (0, 2) are

a) 0, 8

b) 0,-8

c) 1,8

d)1,-8​

Answer 1

Answer:

this answer is correct (c)

Step-by-step explanation:

❤by❤☺

Answer 2

d). The greatest and the least value of$f(x) = x^{4} - 8x^{3} + 22x^{2} - 24x + 1$ in (0, 2) are 1, -8

Given:

$f(x) = x^{4} - 8x^{3} + 22x^{2} - 24x + 1$

Range (0,2)

To find:

Least and greatest values between (0,2).

Solution:

Case 1 - x = 0

$f(x) = x^{4} - 8x^{3} + 22x^{2} - 24x + 1\\\\f(0) = 0^{4} - 8(0)^{3} + 22(0)^{2} - 24(0) + 1\\\\f(0) = 1$

Case 2 - x = 1

$f(x) = x^{4} - 8x^{3} + 22x^{2} - 24x + 1\\\\f(1) = (1)^{4} - 8(1)^{3} + 22(1)^{2} - 24(1) + 1\\\\f(1) = 1 - 8 + 22 - 24 + 1\\\\f(1) = - 7 - 2 + 1\\\\f(1) = - 9 + 1\\\\f(1) = - 8$

Case 3 - x = 2

$f(x) = x^{4} - 8x^{3} + 22x^{2} - 24x + 1\\\\f(2) = (2)^{4} - 8(2)^{3} + 22(2)^{2} - 24(2) + 1\\\\f(2) = 16 - 64 + 88 - 48 + 1\\\\f(2) = -7$

As, we have found values of three cases in (0,2) we saw that x = 0 gave greatest and x = 1 gave least value which are 1 and -8 respectively.

Therefore, the greatest and the least value of$f(x) = x^{4} - 8x^{3} + 22x^{2} - 24x + 1$ in (0, 2) are 1, -8