1. Find values of a,b,c, and d such that g(x) = a(x^3)+b(x^2)+cx+d has a local maximum at (2,4) and a local minimum at (0,0)

Question

2. Need someone to explain this. Graph a function f(x) for which:
f(3)=f(5)=0
f'(x)<0 if x<4
f'(4)=0
f'(x)>0 if x>4
f"(x)>0 for all x

I know there is concave up/down, zeros and turning points involved but i'm just unsure how to graph it as listed.

3. Find the equation of the tangent to the curve y=e^(2x-1) at the point where x=2.
So to find the derivative of y=e^(2x-1), after I use log/ln then what?

On the second, sketch the points you know, and the shapes, then connect them.
on the first..
Take the first and second derivatives. Set the first to zero, an solve for roots at x=2, 0. You can use the second derivative to assist.

On the third. You know the slope (the value of the derivative at x=2)
so y=mx + b you know y, m, x at the point of tangency, solve for b.