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The equation 2x^2 + 2kx + (k + 2) = 0, where k is a constant, has two distinct real roots. Show that k satisfies k^2 – 2k – 4 > 0

Two distinct real roots means that we can use b^2-4ac>0 relationship for any ax^2+bx+c equation. Apply the above gives, 4k^2 - 4 2 (k+2)>0 Simplifying gives, k^2 - 2k -4 >0
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Answered by Andreas T. • Maths tutor
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How to find and classify stationary points (maximum point, minimum point or turning points) of curve.

To find the stationary points of a function we must first differentiate the function. The derivative tells us what the gradient of the function is at a given point along the curve. Therefore, should we find ...
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Answered by Callum J. • Maths tutor
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Find the equation of the tangent to the curve y = (2x -3)^3 at the point (1, - 1), giving your answer in the form y = mx + c.

y = (2x -3)^3 y = (2x)^3 + 3.((2x)^2)(-3) + 3.(2x).(-3)^2 + (-3)^2 using Pascal's Triangle. y = 8x^3 - 36x^2 + 54x - 27 dy/dx = 24x^2 - 72x + 54 at point (1,-1); dy/dx = 24 -72 + 54 = 6 Therefore tangent lin...
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Answered by Robert S. • Maths tutor
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Find the first derivative of y=2^x

There is an initial subtle difficulty to this question, and it highlights understanding of the relationship between natural logarithms and the exponential function. One of the ways to solve this question, is...
AM
Answered by Alex M. • Maths tutor
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Find the general solution of 2 dy/dx - 5y = 10x

Try y=Ae bx diffrentiate this (dy/dx = Abe bx ) and sub into 2dy/dx -5y = 0 to find complementary function. 2Abe bx - 5Ae bx = 0 2b - 5 = 0 b = 2.5 Find the particular integral using trial solution y = Cx+D,...
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Answered by Amy H. • Maths tutor
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