Slope of the Curve | MATHalino reviewer about Slope of the Curve

The slope of $y = f(x)$ is $y' = f'(x)$

Problem
Find the slope of the curve $x^2 + y^2 - 6x + 10y + 5 = 0$ at point $(1, \, 0)$.

A. 2/5	C. -5/2
B. 1/4	D. 2

Problem
Find the equation of the curve passing through the point (3, 2) and having s slope 5x² - x + 1 at every point (x, y).

A. $y = \frac{5}{3}x^3 - \frac{1}{2}x^2 + x - \frac{31}{3}$	C. $y = 5x^3 - 2x^2 + x - 118$
B. $y = 5x^3 - 2x^2 + x - 31$	D. $y = \frac{5}{3}x^3 - \frac{1}{2}x^2 + x - \frac{83}{2}$

Problem
A point moves in the plane according to equations x = t² + 2t and y = 2t³ - 6t. Find dy/dx when t = 0, 2, 5.

A. -3, -3, -12	C. 3, 3, 12
B. 3, -3, 12	D. -3, 3, 12