1. `y=x^3+6x^2-15x+7`
Find Second Derivative

Solution:
`d/(dx)(x^3+6x^2-15x+7)`

`=d/(dx)(x^3)+d/(dx)(6x^2)-d/(dx)(15x)+d/(dx)(7)`

`=3x^2+12x-15+0`

`=3x^2+12x-15`

Now, `d^2/(dx^2)(x^3+6x^2-15x+7)=d/(dx)(3x^2+12x-15)`

`=d/(dx)(3x^2)+d/(dx)(12x)-d/(dx)(15)`

`=6x+12-0`

`=6x+12`

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2. `y=x^3-9x^2+24x+2`
Find Second Derivative

Solution:
`=x^3-9x^2+24x+2`

`d/(dx)(x^3-9x^2+24x+2)`

`=d/(dx)(x^3)-d/(dx)(9x^2)+d/(dx)(24x)+d/(dx)(2)`

`=3x^2-18x+24+0`

`=3x^2-18x+24`

Now, `d^2/(dx^2)(x^3-9x^2+24x+2)=d/(dx)(3x^2-18x+24)`

`=d/(dx)(3x^2)-d/(dx)(18x)+d/(dx)(24)`

`=6x-18+0`

`=6x-18`

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3. `y=4x^3+19x^2-14x+3`
Find Second Derivative

Solution:
`=4x^3+19x^2-14x+3`

`d/(dx)(4x^3+19x^2-14x+3)`

`=d/(dx)(4x^3)+d/(dx)(19x^2)-d/(dx)(14x)+d/(dx)(3)`

`=12x^2+38x-14+0`

`=12x^2+38x-14`

Now, `d^2/(dx^2)(4x^3+19x^2-14x+3)=d/(dx)(12x^2+38x-14)`

`=d/(dx)(12x^2)+d/(dx)(38x)-d/(dx)(14)`

`=24x+38-0`

`=24x+38`

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4. `y=3x^2+12x-15`
Find Second Derivative

Solution:
`=3x^2+12x-15`

`d/(dx)(3x^2+12x-15)`

`=d/(dx)(3x^2)+d/(dx)(12x)-d/(dx)(15)`

`=6x+12-0`

`=6x+12`

Now, `d^2/(dx^2)(3x^2+12x-15)=d/(dx)(6x+12)`

`=d/(dx)(6x)+d/(dx)(12)`

`=6+0`

`=6`

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