Mathematics Calculus

Question

Find an equation of the tangent line to the graph of f (x) = x² + 8 at the point (1,9).

a) y = 2x

b) y = 2x + 7

c) y = 9x + 8

d) x = 2y -17

Answer 1

To find the tangent line to the graph of f(x)=x²+8 at the point (1,9), start by taking the derivative of f(x):

f'(x)=2x

Recall that f'(x) represents the slope of the tangent line. Since the x-value of our given point is 1, plug in 1 for x into the derivative:

f'(1)=2(1)=2

So the slope of the tangent line at the point (1,9) is 2.

Next use the point-slope equation of a line:

y-y₁=m(x-x₁)

Substitute m=2, x₁=1, and y₁=9:

y-9=2(x-1)

Use the distributive property on the right side of the equation:

y-9=2x-2

Add 9 to both sides of the equation:

y=2x+7