Calculus Question

Question

Find the slope of the tangent to the curve f(x) = x²-2x-1 at the point (3,2)

Answer 1

We find the derivative of the function

y' =2x-2.

 

The value of the derivative at any point is the value of the tangent slope. The point in question is (3, 2). So, x=3.

 

We evaluate:

y'(3)=2•3-2=4.

 

You can put that slope in the equation of the tangent line and find it.

 

The slope is 4.

Answer 2

The tangent line is

 

y - y₁ = f'(3)(x - x₁)

 

where:

f'(3) is the derivative at x=3

(x₁ , y₁) is (3, 2)