How do you find f'(-1) using the limit definition given #-5x^2+8x+2#?

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Answer 1 · 2017-02-12T15:35:14

#f(-1) = 18#

The limit definition implies the formula #f'(x) = lim_(h->0) (f(x + h) - f(x))/h#.

#f'(x) = lim_(h->0) (-5(x + h)^2 + 8(x + h) + 2 - (-5x^2 + 8x + 2))/h#

#f'(x) = lim_(h->0)(-5(x^2 + 2xh + h^2)+ 8x + 8h + 2 +5x^2 - 8x - 2)/h#

#f'(x) = lim_(h->0)(-5x^2 - 10xh - h^2 + 8x - 8x + 2 - 2 + 8h + 5x^2)/h#

#f'(x) = lim_(h->0) (-10xh + 8h)/h#

#f'(x) = lim_(h->0) (h(8 - 10x))/h#

#f'(x) = 8 - 10x#

We can evaluate through substitution.

#f'(-1) = 8 - 10(-1) = 18#

Hopefully this helps!