Question

Finding an Equation of a Tangent Line In Exercise, find an equation of the tangent line to the graph of the function at the given point. See Example 5.

y = ln x5/2; (1, 0)

Answer 1

Answer: y = 2.5(x-1)

Explanation:

Step 1

Find the point of tangency.

It's given as (x,y)= (1,0)

Step 2

Find the first derivative, and evaluate it at x=1

f'(x) = 5/2 × d(lnx)/dx = 5/2 × 1/x = 5/2x

f'(x) = 5/2 = 2.5

The slope of the tangent line at this point is m= 2.5

Step 3

Find the equation of the tangent line at (1,0) with a slope of m=2.5

y−y1 = m(x - x1)

y-0 = 2.5(x-1)

y = 2.5(x-1)