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Find the approximate value of f(3. 02...

Find the approximate value of `f(3. 02)` , where `f(x)=3x^2+5x+3` .

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Here `x = 3 , Deltax = .03`
`Deltay = f(x + Deltax) - f(x) " " ... (i)`
`(dy)/(dx) = f'(x)`
=6x + 5
`Delta y = (f'(x))_(x = 3) Delta x`
`=23 xx .03`
`implies Delta y = .69`
`=f (3.03) - f(3) " "` [Using (i)]
`f(3.03) = f(3) + 0.69`
`= 48 + 0.69`
`implies f (3.03) = 48.69`
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