Leaving Cert Higher Level Maths 2021 Question 6

Question 6 from the leaving cert higher level maths paper 1 2021 is a calculus question. In part a we simply need to verify that a graph is the derivative of a function by finding the roots and the y intercept. In part b we find the maximum slope of the function and in part c we use integration to find the original function.

[@LearnwithAI210]

Could you use -b formula for (a) to show the roots or do u have to factorise?

[@jessicac485]

But it says the graph is h'(x) so would the max not be the derivative of h'(x)?? Therefore h''(x)?

[@SimpleScienceandMaths]

There is a local max or min when h'(x)=0, i.e. when the slope is zero, there is only one place where the slope is zero on the graph of h'(x) so that is the max. The second derivative test, h''(x) tells us whether it is a max or min, in this case there is no need to do that.

[@conallwilliamson842]

@@SimpleScienceandMaths You're both right. You could equally differentiate h'(x) to find x = 1 algebraically, rather than reading it from the graph, which I think is what Jessica was asking