Question

пж помогите................

Answer 1

Ответ:

1.

$f(x) = \frac{27x}{ \sqrt[3] {x} } = 27 {x}^{1 - \frac{1}{3} } = 27 {x}^{ \frac{2}{3} }$

$f'(x) = 27 \times \frac{2}{3} {x}^{ - \frac{1}{3} } = \frac{18}{ \sqrt[3]{x} }$

$f'(27) = \frac{18}{ \sqrt[3]{27} } = \frac{18}{3} = 6$

2.

$f(x) = \frac{14x - 1}{x + 0.5}$

$f'(x) = \frac{(14x - 1)'(x + 0.5) - (x + 0.5)'(14x - 1)}{ {(x + 0.5)}^{2} } = \\ = \frac{14(x + 0.5) - (14x - 1)}{ {(x + 0.5)}^{2} } = \\ = \frac{14x + 7 - 12x + 1}{ {(x + 0.5)}^{2} } = \frac{2x + 8}{ {(x + 0.5)}^{2} }$

$f'(1.5) = \frac{2 \times 1.5 + 8}{(1.5 + 0.5) {}^{2} } = \frac{3 + 8}{ {2}^{2} } = \\ = \frac{11}{4} = 2.75$

3.

$f(x) = ( {x}^{2} - 1)(2 - 3x)$

$f'(x) = ( {x}^{2} - 1)'(2 - 3x) + (2 - 3x)'( {x}^{2} - 1) = \\ = 2x(2 - 3x) - 3( {x}^{2} - 1) = \\ = 4x - 6 {x}^{2} - 3 {x}^{2} + 3 = - 9 {x}^{2} + 4x + 3$

$f'( - 25) = - 9 \times 50 - 100 + 3 = - 550 + 3 = - 547$