"What is the equation of the tangent line..." was answered by our community

chechemua62l

Answered question

2022-03-16

What is the equation of the tangent line of

f (x) = x^{2} - x + 4

at x=2?

Vaspplado8ko

Beginner2022-03-17Added 5 answers

First thing to remember is that f'(x)=m (the slope) and that the equation of a line is y=mx+b
So,

f (x) = x^{2} - x + 4 \Rightarrow f^{'} (x) = 2 x - 1

Since f'(x)=m, at x=2, we have, m=2(2)-1=3
From our equation,

f (x) = x^{2} - x + 4

, we know that f(x) is another way of writing y, so,

f (x) = y = x^{2} - x + 4

and at x=2, we have,

y = {(2)}^{2} - 2 + 4 \Rightarrow y = 6

Now, to write our equation, all we have to do is to find b from y=mx+b (with y=6, m=3 and x=2)

y = m x + b \Rightarrow 6 = 3 (2) + b \Rightarrow b = 0

Therefore, our equation will be y=3x

Do you have a similar question?

Recalculate according to your conditions!

Didn't find what you were looking for?