Cách làm cho bạn:
a) \(f(x) = (x + 10)^6\)
Ta có \(f'(x) = 6(x + 10)^5.(x + 10)'=(6x+60).(x + 10)^5\),
\(f"(x) = 6.5(x + 10)'.(x + 10)^4= 30.(x + 10)^4\)
\(\Rightarrow f''(2) = 30.(2 + 10)^4 = 622 080\).
b) \(f(x) = \sin 3x\)
Ta có \(f'(x) = (3x)'.\cos 3x = 3\cos 3x\),
\(f"(x) = 3.[-(3x)'.\sin 3x] = -9\sin 3x\).
\(\Rightarrow f"\left ( -\frac{\pi }{2} \right ) = -9\sin \left ( -\frac{3\pi }{2} \right ) = -9\);
\(\Rightarrow f"(0) = -9sin0 = 0\);
\(\Rightarrow f" \left ( \frac{\pi }{18} \right ) = -9\sin\left ( \frac{\pi }{6} \right ) = -\frac{9}{2}\).
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