# Free Response Questions for BC Calculus

• January 13th 2009, 07:22 PM
rocsfinest762
Free Response Questions for BC Calculus

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.
• January 13th 2009, 07:28 PM
Prove It
Quote:

Originally Posted by rocsfinest762

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.

1. a) Perpendicular lines have gradients that have a product of -1.

So find $\frac{dy}{dx}|_{x = 2}$, then find its negative reciprocal. This is the gradient of the line that is perpendicular. Then use the point (2, 3) along with the gradient in the formula

$y - y_1 = m(x - x_1)$

to find the equation of the line.