Find an equation of the tangent line to the graph of the function f defined by the following equation at the indicated point.

Question

Find an equation of the tangent line to the graph of the function f defined by the following equation at the indicated point.

y² − x² = 25; (5, 5 square root 2)

y= ?

Answer 1

2yy' - 2x = 0 is the IMPLIED derivative

Plugging in...

2( 5 sqrt(2)) y' - 2(5) = 0

10 sqrt(2) y' - 10 = 0

sqrt(2) y' = 10/10 = 1 <--- adds 10 to both sides and then divides both sides by 10

2 y' = sqrt(2) <--- rationalizes the denominator by multiplying both sides by sqrt(2)

y' = sqrt(2) /2 = m is the slope

Point slope form is :

y - 5*sqrt(2) = [(sqrt(2))/2] (x - 5)

adds 5 sqrt(2) to both sides:

y = [(sqrt(2))/2] (x - 5) + 5 * sqrt(2)

distributive says:

y = [(sqrt(2))/2] (x) - (5/2) sqrt(2) + 5 * sqrt(2)

y = [(sqrt(2))/2] (x) + (5/2) * sqrt(2)