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Find the tangent to the curve y=(3/4)x^2 -4x^(1/2) +7 at x=4, expressing it in the form ax+by+c=0.

In general, the equation of a line is y-y0=m(x-x0), where m is the gradient and (x0,y0) is a point on the line. We need to find the gradient and a point on our tangent. Step 1: Find gradient. Since our tange...
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Answered by Eleni P. • Maths tutor
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Find the roots of the following quadratic equation: x^2 +2x -15 =0

The question asks for the roots, this simply means the numbers that could replace x in the equation and the result = 0. There are two ways too do this, firstly either using the Quadratic formula, or my facto...
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Consider the function f (x) = (2/3) x^3 + bx^2 + 2x + 3, where b is some undetermined coefficient: (a) find f'(x) and f''(x) and (b) if you know that f(x) has a stationary point at x = 2, use this information to find b.

(a) We have f(x)=(2/3)x 3 + bx 2 + 2x +3. First we have to solve for f'(x)=(dy/dx)f(x) which gives:f'(x) = [(3 2)/3]x 2 + 2bx + 2 <=> f'(x)=2x 2 + 2bx + 2 From there we do a second differentiation to s...
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Show that x^2+6x+11 can be written in as (x+p)^2+q, where p and q are integers to be found.

To start, we need to complete the square of the equation. To do this, we divide the coefficient of x by 2. Here, 6/2=3. We then find (x+3)^2, which gives us the first part of the equation we want to express,...
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Answered by Hannelore E. • Maths tutor
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How do I find the co-ordinates of a stationary point of a given line and determine whether it is a minimum or a maximum point?

When you find the first derivative of the equation and equate it to 0 then solve for x, you will find the x-coordinates of the stationary point(s) of the graph. For example, let's say f(x)=-x 3 +x 2 +8x+10 t...
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