Free Response Questions for BC Calculus

I'm having trouble with these problems. I can't even start these problems. Please help me.

1) Given the parabola y = x2 − 2x + 3:

a. find an equation for the line L, which contains the point (2,3) and is perpendicular to the line tangent to

the parabola at (2,3).

b. find area of that part of the first quadrant which lies below both the line L and the parabola.

2) Let f be the function defined for pi/6 < x < 5pi/6 by f(x) = x + (sin^3)x.

a. Find all values of x for which f′ (x) = 1.

b. Find the x-coordinates of all minimum points of f. Justify your answer.

c. Find the x-coordinates of all inflection points of f. Justify your answer.