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Year 12 Maths 2 Unit Hard Maths
Question

Consider the function whose derivative is given by

dydx=x3x-2x+3. Which value of x will give a maximum turning
point on the graph of the function? Explain.

Find the exact volume if the region bounded by the curve y = 3logx ,
the x axis and x = 5, is rotated about the y axis.

Answer

dydx= x3(x-2)(x+3)

 

x-4-3-10123
dydx-384060-40162
  • Maximum turning point at x=0

 

y=3logx

 

 

 

 

 

 

volume=π03log525-ey32dy              =π25Y-e2y32303log5              =π75log5-32e2log5-10-32e0              =π75log5-32×25+32              =π75log5-752+32              =π75log5-722               =π75log5-36u3 

 

 

 

 

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