Slope of the Curve

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

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

 

 
 
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