Consider function to be g(x);

a) Find the values by observing the slope of tangent line to curve graphically:
a) g ' (-1) b) g ' (0) c) g ' (0.5) d) g ' (1)

b) use the four points found in a to sketch graph of g ' (x)

Any nudge in the right direction would be greatly appreciated!

2. Originally Posted by boousaf
Consider function to be g(x);

a) Find the values by observing the slope of tangent line to curve graphically:
a) g ' (-1) b) g ' (0) c) g ' (0.5) d) g ' (1)

b) use the four points found in a to sketch graph of g ' (x)

Any nudge in the right direction would be greatly appreciated!
i hate problems like these. the graphs are never accurate enough to do what they ask you to. just imagine a straight line being drawn at each of the points in the direction the curve is moving. we want to estimate the slope of such a line

these are what the values seem like to me g'(-1) = 2 or matbe 1.5, g'(0) = -1, g'(0.5) = g'(-0.5) = 0, g'(1) = 2 or maybe 1.5

for (b), note that since we have an x^3 graph, the derivative will be an x^2 graph. so just draw one that passes roughly through those points and you're good