Find the point where the graphs of f(x) and g(x) are tangent to each other

Question

Find the point where the graphs of f(x)=x^3-2x and g(x)=0.5x^2-1.5 are tangent to each other (have a common tangent line)

a) use knowledge of the derivative to solve this problem. Write out a complete solution with explanations (solutions by inspections the graph or guessing are not acceptable)

b) illustrate your solution with a graph containing f(x), g(x) and the tangent line found

Answer 1

Please see video.