Given f(x)=3x^2-4x+1, find `lim_(h->0)(f(-1+h)-f(-1))/h`

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justaguide | College Teacher | (Level 2) Distinguished Educator

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The function `f(x)=3x^2-4x+1` .

`lim_(h->0) (f(-1+h)-f(-1))/h `

=> `lim_(h->0)(3*(-1+h)^2-4*(-1+h)+1 - 3*(-1)^2+4*(-1)-1)/h`

=> `lim_(h->0)(3*(-1+h - 1)(-1 + h + 1) + 4 - 4h + 1 - 4 - 1)/h`

=> `lim_(h->0)(3*(-2+h)(h) - 4h)/h`

=> `lim_(h->0)(3*(-2+h) - 4)`

=> 3*-2 - 4

=> -6 - 4

=> -10

The result of `lim_(h->0) (f(-1+h)-f(-1))/h = -10`

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