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vitfil [10]
3 years ago
10

Use the definition of the derviative to compute the derivative of f(x)= 1- 7x^2 at the specific point x=2.

Mathematics
1 answer:
GaryK [48]3 years ago
4 0

Answer:

f'(x) = -28 \ at  \ x = 2

Step-by-step explanation:

f'(2) =  \lim_{h \to 0}\frac{f(2+h)) -f(2)}{h} \\\\f(2+h) = 1 - 7(2+h)^2 = 1 - 7(4 +h^2 +4h) = 1 - 28 - 7h^2 - 28h = - 7h^2 -28h - 27\\\\f(2) = 1 - 7(2^2) = 1 - 28 = -27\\\\f(2+h) - f(2) = -7h^2 - 28h - 27 - (-27) = -7h^2 -28h -27 + 27 = -7h^2 -28h\\\\f'(2) =   \lim_{h \to 0}\frac{-7h^2 - 28h}{h} \\\\

       = \lim_{h \to 0} \frac{h(-7h -28)}{h}\\\\= \lim_{h \to 0} (-7h -28)}\\\\= -7 (0) - 28\\\\= -28

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