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Find the x co-ordinate of stationary point of the graph y=5x^3 +3x

When you differentiate the function that gives the gradient. Therefore differentiate to get dy/dx= 15x^2 + 3. Make this equal to 0 to get 15x^2 + 3=0 and rearrange to get the value of x as required so 15x^2=...
VJ
Answered by Vinay J. • Maths tutor
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Factorise 5a – 3a^2

Answer: a(5-3a)Explanation: We take the highest common factor of both of the terms, which is a and we put it outside of the bracket. Then, in the bracket we put two terms that when multiplied by a, the produ...
CM
Answered by Christina M. • Maths tutor
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Integrate ln(x)

Our A-level knowledge does not give us any identities to be able to integrate this from memory. But what we do have from memory is that the derivative of ln(x) is 1/x. Why would this help us? Let's take a lo...
JE
Answered by James E. • Maths tutor
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Solve the following simultaneous equations: 6j+4k=40; 7j-3k=-7

j = 2, k = 7
CE
Answered by Catherine E. • Maths tutor
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Consider the unit hyperbola, whose equation is given by x^2 - y^2 = 1. We denote the origin, (0, 0) by O. Choose any point P on the curve, and label its reflection in the x axis P'. Show that the line OP and the tangent line to P' meet at a right angle.

We differentiate our equation with respect to x to find that 2x - 2y(dy/dx) = 0, and rearrange to find that dy/dx = x/y. We set P = (x, y). The slope of OP is given by y/x, and the slope of the tangent at P'...
DC
Answered by Dylan C. • Maths tutor
3948 Views