Question

Find the slope of the graph of the function y=5x/x-2 at (3,15). Then find an equation for the line tangent to the graph at that point.

Answer 1

@clavoie slope of the graph can be determined if we differentiate y w.r.t x

Answer 2

wouldn't it be 5?

Answer 3

@clavioe have u applied the quotient rule?

Answer 4

I don't know...I'm taking this class online and I'm so lost right now

Answer 5

If the function f(x) = g(x)/h(x) where h(x) is not equal to zero
then according to quotient rule,
f '(x) = h(x) g'(x) - g(x) h'(x) / {h(x)}^2

Answer 6

try to apply this rule and u will finally get the slope

Answer 7

I have no idea what that is or how to do that. We were given the equation \[\lim f(x _{0}+h)-f(x _{0})/h\] to solve these problems

Answer 8

yeah it is first principle
it will make the solution lil bigger
can u help @gerryliyana

Answer 9

no

Answer 10

can you please just show me the steps on how to solve this?

Answer 11

lets do this ques
can u write f(x+h) ?

Answer 12

f(3+h)= 5(3+h)/3+h-2

Answer 13

cool
now write f(x+h) - f(x) ?

Answer 14

(5(3+h)/3+h-2)-(5(3)/3-2)

Answer 15

can u simplify the above expression?

Answer 16

(15+5h/1+h)-15

Answer 17

take the LCM now and what will u get?

Answer 18

I don't know, this is where I get stuck

Answer 19

f(3+h)-f(3) = {15 + 5h - 15(1+h) } / (1+h)
= {15 + 5h - 15 - 15h } / (1+h)
= -10h/ (1+h)

Answer 20

now f ' (3) = Lim f(3+h)- f(3)/h
hope u will get the slope now

Answer 21

So the slope is -10?

Answer 22

yeah

Answer 23

in order to determine the equation , use point slope form
according to point slope form
y - y1 = m (x-x1)
where m = slope of the line
and (x1, y1) is any point on the line