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Find the minimum and maximum points of the graph y = x^3 - 4x^2 + 4x +3 in the range 0<=x <= 5.

First, use the standard method of setting the derivative to be equal to 0 to find the stationary points. This yields the equation 3x^2 - 8x + 4 = 0 and so the stationary points are at x = 2/3 and 2 respec...

GM
Answered by Guy M. Maths tutor
5365 Views

A curve has equation x = (y+5)ln(2y-7); (i) Find dx/dy in terms of y; (ii) Find the gradient of the curve where it crosses the y-axis.

(i) To find the derivative we will use the product rule. Let u = y+5 and v=ln(2y-7). Then dx/dy = du/dyv + udv/dy = ln(2y-7) + (y+5)*2/2y-7 (used the chain rule in 2nd term - can explain this on ...

SP
Answered by Szymon P. Maths tutor
10144 Views

How does Mary Shelley use her characters in 'Frankenstein' to frame the struggle between religion and science in her society?

Shelley uses Frankenstein’s character as a tool to explore social pressures on natural philosophers, however she resists a portrayal that definitively adheres to a secular or religious position. Frankenst...

WB
Answered by William B. English tutor
2962 Views

How does Emily Dickinson portray the body and soul in 'I'm afraid to own a Body -' (1090)?

Dickinson recurrently uses property and material spaces as metaphors for the body to frame the societal pressures that women faced, effectively transmuting the body into ownable and controllable property....

WB
Answered by William B. English tutor
20122 Views

Name the process by which fatty acids and glycerol enter the intestinal epithelial cell from the lumen of the intestine

Simple diffusion - fatty acids and glycerol are lipophilic and hydrophobic, therefore can diffuse straight through the lipid bilayer membrane of the epithelial cells down the concentration gradient

JD
Answered by Jack D. Biology tutor
11342 Views

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