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C3 OCR question

Sayu-rin

For the graph of y=x(3-x)^1/2

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a) state the values of x for which y exists

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b) find the gradient at the origin

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c) find the coordinates at the maximum point

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d) Use your answers to draw a sketch of the graph

Reply 1

Dragolien

For a), I think the question means the values of x for which y is a real number. If you square-root a negative number, the result is not real, so the answers for a) are when 3-x is positive.

b) and c) require you to differentiate the equation. From that, you can easily work out the answers by inputting x=0 and dy/dx= 0 respectively.

And from these points, you can sketch the graph, marking the roots, the y-intercept, and any turning points.

Reply 2

MiladA

a) Consider the domain of the function (3-x)^1/2.

b) Use the product rule to find dy/dx then substitute x=0 to find the gradient at the origin.

c) Set dy/dx=0 then solve for x.

d) Sketch using the above information.