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Find the coordinates and determine the nature of the stationary points of curve y=(2/3)x^3+2x^2-6x+3

Stationary points occur when dy/dx=0, therefore determine dy/dx first:
dy/dx= 2x²+ 4x - 6
2) solve dy/dx=0 for two values of x (using quadratic formula, if necessary):
(x+...

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Solve for x and y: 2x +5y + 5= 0 , 2y + 31= 5x

For a question like this you should aim to eliminate either x OR y from one equation in order to deduce the value of the other. 1) 2x +5y + 5= 0 , 2) 2y + 31= 5x
Rearrange equation 2) so that 2y +31...

Answered by Tutor114325 D. • Maths tutor

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The normal to the curve x*(e^-y) + e^y = 1 + x, at the point (c,lnc), has a y-intercept c^2 + 1. Determine the value of c.

We firstly need to find the slope of the line normal to the curve at the point (c, lnc). To do this, we will differentiate implicitly the equation of the curve to find the slope of the tangent. By implici...

Answered by Katerina A. • Maths tutor

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A cuboid has length x cm. The width of the cuboid is 4 cm less than its length. The height of the cuboid is half of its length. The surface area of the cuboid is 90 cm^2 . Show that 2x^2 − 6x − 45 = 0

Take each side of the cuboid as an algebraic expression and multiply each by 2 to account for both sides of the shape. For example, (x)(x-4), which could be expanded to x²-4x, and then multipl...

Answered by Tom M. • Maths tutor

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How does one find the equation of a line passing through 2 points of a graph?

The general equation for a line on a graph is: y = mx + b ,where a is called the slope of the graph and b is the y-intercept(or the point where the line crosses the y axis). Let's assume the 2 points have...

Answered by Dimitar D. • Maths tutor

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