Question

for the given function f(x) 2x+3/1-x find the slope of the tangent line at point x=2

Answer 1

1.

$$f(x)=2x+\dfrac{3}{1-x}$$

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

$$slope=f'(2)=2+\dfrac{3}{(1-2)^2}=5$$

$$slope=5$$

2.

$$f(x)=\dfrac{2x+3}{1-x}$$

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

$$=\dfrac{5}{(1-x)^2}$$

$$slope=f'(2)=\dfrac{5}{(1-2)^2}=5$$

$$slope=5$$