10.2: Find the equation of the line tangent to the graph of f at the indicated value of x.

Question

Find the equation of the line tangent to the graph of f at the indicated value of x.

f(x)= 9 − 2 ln x​; x=1

y= ______

Answer 1

f(x) = 9 -2lnx x=1 ln1 =0

f(1) = 9, the point of tangency is (1,9)

f'(x) = the slope = -2/x = -2/1 =-2

the tangent line has slope =-2

y = -2x + b solve for b by plugging in the point (1,9)

9 =-2 + b

b = 9+2 = 11

y=-2x + 11 is the equation of the line tangent to the curve at x=1