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:
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 $\displaystyle A=\frac13 a$