Question

Find the equation of the tangent line to the graph f(x)=(x)/square root of (7-3x) at the point where x=1

Answer 1

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Answer 2

First differentiate the equation to find y' the use slope point form (y-y1)/(x-x1)=y'

Answer 3

how do you take off the square root

Answer 4

why do you need to take off the square root ?differential of sqrt(x)=1/2sqrt(x)

Answer 5

see the differntial of the equation is
y'=(sqrt(7-3x)+(3x/sqrt(7-3x)))/(7-3x)
now put x=1
y'=(2+(3/2))/2
so then slope = 7/4

Answer 6

ohhhhh I GET IT thx :)

Answer 7

ohh but im supose to give the equation of the tangent line ( y=mx+b) if I have only the slope and how am i supose to find the b

Answer 8

now you know slope of the line
then , x=1 so y=1/sqrt(4),y=1/2
so now you have a point and you have the slope.