Question

Im not sure how to approach this problem.
f(1) = 4 and f'(1)= 2 find an equation of the tangent line at x=1 Im not sure how to approach this problem.
f(1) = 4 and f'(1)= 2 find an equation of the tangent line at x=1 @Mathematics

Answer 1

If i had said, "the slope of the line is 2, and the line goes through the point (1,4), what is the equation of the line" could you solve that?

Answer 2

Use the point slope formula for a line, using f'(1) = 2 as the slope.

Answer 3

Oh wow.... thats easy then.

Answer 4

After all the derivative of a function at a point is the slope of the tangent at that point, and the tangent must also pass through the point.

Answer 5

The equation of the tangent line is


y - y1 = m(x - x1)


where the tangent line touches the graph of y = f(x) at the point (x1, y1). Also, the slope is m = f'(x1)


In your case, (x1, y1) = (1, 4), so x1 = 1 and y1 = 4


Also, m = f'(x1) = f'(1) = 2, so m = 2


Plug all this into y - y1 = m(x - x1) to get



y - y1 = m(x - x1)


y - 4 = 2(x - 1)


Now solve for y



y - 4 = 2x - 2


y = 2x - 2 + 4


y = 2x + 2


So the equation of the tangent line is y = 2x + 2

Answer 6

aha, thank you guys. it was just worded odd to me. *sigh*