Question

Determine the equation of the tangent line to f(x)=4x^2-2x+13 at x=2

I am looking at old exams to study for my final and they have the answer as y=14(x-2)+25. I was wondering how did they get that?

Answer 1

1/ replace x =2 to find f(2), from then you have a point (2, f(2))
2/take derivative of f(x) , it is f'(x) and replace x =2 into it to get the slope of the tangent line
3/ replace the point (2, f(2) ) and the slope (from step 2) into the formula of y - y_0 = m (x -x_0) to get the answer.

Answer 2

Thank you!