Practice IB Mathematics Analysis and Approaches (AA) Topic SL 5.6—differentiating Polynomials n E Q. Chain, Product and Quotient Rules with authentic exam-style questions for both SL and HL students. This question bank focuses on the exact syllabus content for SL 5.6—differentiating Polynomials n E Q. Chain, Product and Quotient Rules and mirrors Paper 1, 2, 3 style where relevant.
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Let .
Show that .
Show that .
Hence, using your answer from Part 2, find in terms of .
Let for .
Find .
Find the equation of the tangent at .
Let , for . The region is bounded by the graph of , the x-axis, and the lines and .
Find .
Show that the area of is .
Find the x-coordinate where the tangent to is horizontal.
Let and . Both and are differentiable at .
Find .
Determine whether the gradients of the tangents to and at are equal.
Find the equation of the tangent to at .
Consider the function , for .
Show that .
Find the coordinates of the point where the tangent to the graph is horizontal.
Sketch the graph of , indicating the x -intercept and the point from part 2.