Table of Contents
T15
Najděte lokální extrémy funkcí:
181.
\( f(x) = \frac{x^2 − 3x + 2}{x^2 + 2x + 1} \) f(x) = (x^2 − 3x + 2)/(x^2 + 2x + 1)
182.
\( f(x) = \sqrt{2x − x^2} \) f(x) = sqrt(2x − x^2)
183.
\( f(x) = x \sqrt[3]{x − 1} \) f(x) = x cuberoot (x − 1)
171.
\( f(x) = 2 + x − x^2 \) f(x) = 2 + x − x^2
172.
\( f(x) = (x − 1)^4 \) f(x) = (x − 1)^4
173.
\( f(x) = x^m (1 − x)^n , m, n \in N \) f(x) = x^m (1 − x)^n
174.
\( f(x) = \cos x + \cosh x \) f(x) = cos x + cosh x
184.
\( f(x) = xe^−x \) f(x) = xe^−x
175.
\( f(x) = (x + 1)^10 e^−x \) f(x) = (x + 1)^10 e^−x
185.
\( f(x) = \frac{ln^2 x}{x} \) f(x) = ln^2 x / x
176.
\( f(x) = |x| \) x|
177.
\( f(x) = x^\frac{1}{3} (1 − x)^\frac{2}{3} \) f(x) = x^1/3 (1 − x)^2/3
186.
\( f(x) = \cos x + \frac{1}{2} \cos 2x \) f(x) = cos x + 1/2 cos 2x
187.
\( f(x) = \frac{10}{1 + \sin^2 x} \) f(x) = 10/(1 + sin^2 x)
178.
\( f(x) = x^3 − 6x^2 + 9x − 4 \) f(x) = x^3 − 6x^2 + 9x − 4
179.
\( f(x) = x(x − 1)^2 (x − 2)^3 \) f(x) = x(x − 1)^2 (x − 2)^3
180.
\( f(x) = x + \frac{1}{x} \) f(x) = x + 1/x
188.
\( f(x) = \atan x − \frac{1}{2} \ln(1 + x^2) \) f(x) = atan x − 1/2 ln(1 + x^2)
189.
\( f(x) = e^x sin x \) f(x) = e^x sin x
