Let `f(x)={x^3-x^2+10 x-5,xlt=1-2x+(log)_2(b^2-2),x >1` Find the values of `b` for which `f(x)` has the greatest value at `x=1.`

Options

A. `1leble2`
B. `b={1, 2}`
C. `bin(-oo, -1)`
D. None of these

Answer

D

Explanation

for x `le` 1
f'(x) = `3x^(2)-2x+10=3[(x-(1)/(3))^(2)+(24)/(3)]gt0`
`therefore` f(x) is `uparrow"fx"^("n")`
For x `gt` 1, f'(x) `lt` 0
`therefore` f(x) has greatest value at x = 1
`underset(xto1^(@))(lim)` f(x) `le` i(1)
`rArr -2+log_(2)(b^(2)-2)le5`
`log_(2)(b^(2)-2)le7`
`b^(2)le130" but "b^(2)gt2`
`2leb^(2)le130`
`bin[(-sqrt(130),-sqrt(2))uu(sqrt(2),sqrt(130))]`