1. 9the tangent line to the graph y= cuberoot(xy=cuberootx) at the point(8,24) has the form y=mx+b. what is m+b?
2. Graph the function f(x) passes through (0,3). The tangent line at this point also passes through the point (3,9). What is f'(0)?
3. The functionf(x) =ax³+bx satisfiesf'(0) = 1 andf''(1) = 12 What isa+b?
4. In order to smash a pumpkin, you drop it from a very tall tower. If the tower has heightC (in meters), then the height of the pumpkin will beH(t)=C5t² aftertseconds. If you want the pumpkin to be traveling at 100 meters per second, at the moment it hits the ground, how high must the tower be?
5. Iff(x) = sin(x) , then what isf'()?
6. Iff(x) =x^ln(x) then what isf'(e)?