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A cubic curve has equation y x3 3x2 1. (i) Use calculus to find the coordinates of the turning points on this curve. Determine the nature of these turning points.

y′=3x2 −6x use of y′ = 0 0= 3x^2 - 6x 0= 3x(x-2) therefore either x=0 or x=2 when x=0 y=1, when x=2 y=-3 (0, 1) or (2, −3) y''=6x-6 when x=0 y''=6(0)-6 = -6 as y'' is negative this means at x=o the curve is ...
CB
Answered by Charlotte B. • Maths tutor
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Why does the reactivity of group 1 elements increase as you go down the group?

Group 1 metals all have one electron in their outer shell. When they react they form positive metal ions by losing this electron. Since there is only one electron to lose, group 1 metals are all extrememely ...
PH
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How and why does an increase in temperature effect the rate of an enzyme substrate reaction?

As temperature increases up to the optimal temperature for the enzyme, the rate of reaction will increase at a steady rate because the kinetic energy of the enzyme and substrate molecules increases, so there...
ES
Answered by Edward S. • Biology tutor
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How do I answer a legal problem question?

Remember I-P-A! (1) ISSUE: which area of law does the question concern? What does the party you are acting for wish to achieve? E.g. "C wishes to establish D was negligent in hitting her with his car, i...
MJ
Answered by Megan J. • Law tutor
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How is heart rate controlled?

It can be controlled by hormonal or neuronal (from the nervous system) input. To increase the heart rate, during a fight or flight situation for example, adrenaline may be released from the adrenal glands an...
GM
Answered by Grace M. • Biology tutor
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