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.
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
1 answer