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The equation x^2+ kx + 8 = k has no real solutions for x. Show that k satisfies k^2 + 4k < 32.

If a quadractic equation ax^2 + bx + c = 0 has no real solutions, this means that the discriminant is less than 0, i.e. b^2-4ac<0. Let's put our equation in this form: x^2 + kx + 8 = k rearranges to x^...

Answered by Tutor91955 D. • Maths tutor

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Find the equation of the tangent to the curve y^3 - 4x^2 - 3xy + 25 = 0 at the point (2,-3).

This is an example of implicit differentiation where we have to consider both the y-terms as well as the x-terms. The first step is to deal with each term on the left hand side individually. This gives us...

Answered by Tanmayi J. • Maths tutor

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Differentiate with respect to x: (6x + 7)e^x

Product Rule: dy/dx (uv) = u'v + uv'
Let u = 6x+7 and v = e^x. Using simple disintegartion, u' is 6 and v' is e^x.
Therefore, answer is: 6e^x + (6x +7)e^x

Answered by Aisha R. • Maths tutor

3291 Views

How do I integrate cos^2x with respect to x?

This can be a very tricky question if you do not know how to approach it. Our first instinct may be to try a substitution, but this gets us nowhere. In fact, the trick is to make use of the identity

Answered by Raiad S. • Maths tutor

11109 Views

Point P on the curve, x = 2tan( y+ π/12), has a y-coordinate of π/4. Find an equation for the normal to the curve at P.

Step 1 - Firstly, we need to find the x-coordinate of point P. This will allow us to find the normal equation required in the question. To find the x-coordinate, we plug in the value of y given in the que...

Answered by Andrew M. • Maths tutor

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