Posted by **Liz** on Saturday, June 30, 2012 at 2:17pm.

Find an equation of the line that is tangent to the graph of f and parallel to the given line.

Funtion:

f(x)=1/sqrt(x-1)

Line:

x+2y+7=0

- Calculus -
**bobpursley**, Saturday, June 30, 2012 at 5:05pm
f'=-1/2 * (x-1)^-1.5

that is the slope then tangent to the line.

y=-x/2-3.5

so slope is -1/2

f'=-1/2 * (x-1)^-3/2=-1/2

solving, x=2

then

y=1/sqrt(x-1)=1 so the point of tangency is 2,1

y=mx+b

2=-1/2 (1)+b

b=2.5

y=-x/2+2.5

check all this.

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