Question

Find the slope of the tangent line to the graph y = x-3 at the point (0.5, 8).

Answer 1

the slope of a line ... is just the slope of the line.

Answer 2

what is the derivative of y with respect to x?

Answer 3

cant you not find the derivative because it would just because 1x^0+ 3^0----- ...........

Answer 4

spose we use first principles ... the slope of a line between 2 points such that the distance between them approaches zero, let h be the difference between them \[\lim_{h\to 0}\frac{f(x+h)-f(x)}{x+h-x}\]
\[\lim_{h\to 0}\frac{[(x+h)-3]-[x-3]}{h}\]
\[\lim_{h\to 0}\frac{x+h-3-x+3}{h}\]
\[\lim_{h\to 0}\frac{h}{h}\]
\[\lim_{h\to 0}1=1~:~for~all~x\]

Answer 5

it we use rules:

for any constant k, k' = 0
for any power of x, other than 0, (x^n)' = n x^(n-1)

y = x^1 - 3

y' = 1x^0 - 0 = 1

Answer 6

the power rule works for x^0 but there is some argument over an indeterminant 0^0 form so they like to avoid it and split the rule into 2 cases