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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...

Answered by Guy M. Maths tutor
5165 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 ...

Answered by Szymon P. Maths tutor
9720 Views

Solve the equation: log5 (4x+3)−log5 (x−1)=2.

As both terms on the left hand side have base 5 we know we can combine them. When dealing with logs, a minus means we can divide them, and a plus means we can multiply them. This will leave us with log5(4...

Answered by Hugh G. Maths tutor
8230 Views

Show that 1+cot^2(x)=cosec^2(x)

Need to remember that:sin2(x)+cos2(x)=1 (eq.1)Divide the whole eq.1 by sin2(x)to get:sin2(x)/sin2x+cos2(x)/sin2(x)=1 /sin2...

Answered by Tutor114151 D. Maths tutor
49822 Views

The mean of 4 numbers is 8 when a 5th number is added the mean becomes 10, what is the 5th number?

Ok, so firstly let's think about what the mean means? Add all the numbers together and then divide by the total number of values we have.So, that means with the 4 numbers we currently have the total divid...

Answered by Carmen O. Maths tutor
6946 Views

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