Equation of Tangent

Question

Given that  𝑓′(2)=2 and  𝑓(2)=1 , find the equation of the tangent line to the curve  𝑦=𝑓(𝑥) at  𝑥=2.

Group of answer choices

1. 𝑦=2𝑥+1
2. 𝑦=2𝑥−1
3. 𝑦=2𝑥+3
4. 𝑦=2𝑥−3
5. 𝑦=2𝑥+2
6. 
   

Answer 1

y=2x-3

f'(2) = 2 = the slope of the tangent line

at x=2 y=f(x)= f(2) = 1

y=2x - 3 = 2(2)-3 = 4-3 = 1

Answer 2

At (2, 1) the slope of the tangent is f'(2) = 2.

Use point-slope form from Algebra 1.