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If f(x)=2x^3-13 x^2+17 x+12 ,\ find f(2...

If `f(x)=2x^3-13 x^2+17 x+12 ,\ ` find `f(2)` (ii) `f(-3)`

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To solve the problem, we need to evaluate the function \( f(x) = 2x^3 - 13x^2 + 17x + 12 \) at two different values: \( f(2) \) and \( f(-3) \). ### Step-by-Step Solution: 1. **Calculate \( f(2) \)**: - Substitute \( x = 2 \) into the function: \[ f(2) = 2(2)^3 - 13(2)^2 + 17(2) + 12 ...
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Knowledge Check

  • If f(x)=(x-1)(2x-3), x in [1,3] , then

    A
    Rolle's theorem is not satisfied in [1,3]
    B
    Rolle's theorem is satisfied in [1,3]
    C
    f(1)=f(3)
    D
    f is not continuous on [1,3]

  • If f(x)=3x^(4)+4x^(3)-12x^(2)+12 , then f(x) is

    A
    increasing in `(-oo,2) and ` in (0,1)
    B
    increasing in (-2,0) and in `(1,oo)`
    C
    decreasing in `(-2,0) and `in (0,1)
    D
    decreasing in `(-oo,-2) and `in (1,`oo`)

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