1. ## Question about Tangent lines

Dear All, I am experiencing trouble with a tangent line problem, can anyone give me advice how to approach the problem? Thank you ! 謝謝你

Question:

2. Originally Posted by mak15
Dear All, I am experiencing trouble with a tangent line problem, can anyone give me advice how to approach the problem? Thank you ! 謝謝你
1. Re-write the equation of the function: $\displaystyle f(x) = -ax^2+7a$

The graph of this function is a parabola. If a < 0 then the parabola opens down, else it is opening upward.

2. Calculate the coordinates of the tangent point: T(-1, f(-1))

3. Determine the first derivative of f and calculate the slope of the tangent line:

$\displaystyle m_t = f'(-1)$

4. Use point-slope-formula to get the equation of the tangent line.

(I've got: $\displaystyle t(x) = y = 2ax + 8a$)

5. Calculate the y-intercept which is t(0).

6. Calculate the x-intercept which is the solution of the equation t(x) = 0

7. Calculate the area by:

$\displaystyle A = \int_{-1}^0(t(x)-f(x))dx$

I've got $\displaystyle A=\frac13 a$