Given the function f(x)=λx^3 + 9, for λ other than zero, find the inflection point of the graph in terms of λ. How does the slope of the line tangent to the inflection point changes as λ varies from 0 to 1?
f'(x) = 3λx^2f''(x) = 6λxFor the inflection point (x0,y0), it is true that f''(x0)=0 so 6λxo=0 => x0= 0 (since λ cannot be zero)Therefore, the infelction point is (0,f(0)) => (0,9)The second part of the question is a trick question since any line tangent to th einfelction point of a graph is parallel with the x'x axis.
