Question

1) a- find the slope of the tangent to the curve y= 3 + 4x^2- 2x^3at the point where x=a
b- find the equations of the tangent lines at the points (1,5) and(2,3)
c- Graph the curve and both the tangent on a common screen

2) if a rock is thrown upward on the planet mars with a velocity of10 m/s, its height( in feet) after t seconds is given by h= 10t-1.8t^2
a-find the velocity of the rock after one second
b- find the velocity of the rock when t = a
c-when will the rock hit the surface
d- with what velocity will the rock hit the surface


3) a-find an equation of the tangent line to the graph of y= g(x)at x =5 if g(5)=-3 and g'(5)=-4
b-if the tangent like to y = f(x) at (4,3) passes through the point(0,2) find f(4) and f'(4)