Question

Решите 3 и 7 пример, даю 59 баллов

Answer 1

3.
$f(x)=(3-x)(2x+1)=6x+3-2x^2-x=-2x^2+5x+3\\ f'(x)=-4x+5\\ f'(2)=-4*2+5=-3$
7.
$f(x)= \sqrt{1-7x}\\ f'(x)= -\frac{7}{2 \sqrt{1-7x}}\\ f'(-9)= -\frac{7}{2 \sqrt{1-7*(-9)}}=- \frac{7}{2 \sqrt{64} }= -\frac{7}{2*8}= -\frac{7}{16}$

Answer 2

$3)\; \; f(x)=(3-x)(2x+1)\; ,\; \; x_0=2\\\\f'(x)=-(2x+1)+(3-x)\cdot 2=-2x-1+6-2x=-4x+5\\\\f'(2)=-8+5=-3\\\\7)\; \; f(x)= \sqrt{1-7x} \; ,\; \; x_0=-9\\\\f'(x)= \frac{1}{2\sqrt{1-7x}} \cdot (-7)=- \frac{7}{2\sqrt{1-7x}} \\\\f'(-9)= -\frac{7}{2\sqrt{64}} =- \frac{7}{2\cdot 8} =-\frac{7}{16}$

$8)\; \; f(x)=(4x-5)^4\; ,\; \; x_0=1\\\\f'(x)=4(4x-5)^3\cdot 4\\\\f'(1)=4(-1)^3\cdot 4=-16$