Use the definition of continuity and the properties of limits to show that the function is continuous at the given number a. x1limf(x)f(x)=(x+3x3)4,a=1=x1lim(x)4=(x1lim(=(x1lim(x)+x1lim(x)bythepowerlaw=(x1lim(x)+(=(1+3()x1(x3))4bythesumlaw= Find f(1)

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Use the definition of continuity and the properties of limits to show that the function is continuous at the given number

a

.

x \to - 1 lim f (x) f (x) = (x + 3 x^{3})^{4}, a = - 1 = x \to - 1 lim (x)^{4} = (x \to - 1 lim (= (x \to - 1 lim (x) + x \to - 1 lim (x) by the power law = (x \to - 1 lim (x) + (= (- 1 + 3 ()_{x \to - 1} (x^{3}))^{4} by the sum law =

Find

f (- 1)

. Find

f

.

f^{''} (x) = 36 x^{2} + 2 x + 6, f (1) = 5, f^{'} (1) = - 2

f (x) =

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