Calculus

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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 -

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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