Question

Find an equation of the tangent line to the graph f at the indicated point. f(x) = xsquared + 1, (2,5)

Answer 1

y = x² + 1
dy/dx = 2x
x = 2, so dy/dx (the slope) = 4

Plug this into point slope form:
y-y₁ = m(x-x₁)

Answer 2

how do i plug this into point slope form?

Answer 3

The point (2,5) and the slope 4 (The slope came from the derivative)

Answer 4

oh of course! that makes sense...I'm clearly not thinking today. Thanks!

Answer 5

m = slope of tangent line
m =dy/dx= 2x=4 (2,5)
5 = 4 2 + b
y=4x-3

Answer 6

This is a direct consequence that the tangent line must intersect the curve at (2,5)