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10-06-2016
Mathematics

contestada

Use the lim f(x)-f(a)/x-a to find the derivative.
x->a

f(x)=-3x^2-5x+1 and point (1,-7)

Respuesta :

10-06-2016

Hello,

f(x)-f(a)= -3x²-5x+1-(-3a²-5a+1)=-3(x²-a²)-5(x-a)=-3(x-a)(x+a)-5(x-a)
=-(x-a)(3(x+a)+5)
=-(x-a)(3x+3a+5)

lim (f(x)-f(a))/(x-a)=- lim (3x+3a+5)=3a+3a+5=-6a-5
if a=1==>-6*1-5=-11

Otherwise
f'(x)=-6x-5
f'(1)=-6-5=-11

at point(1,-7)

Answer Link

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