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For a curve of gradient dy/dx = (2/ (x^2))-x/4, determine a) … a) Differentiating gives d 2 y/dx 2 =-4x-3-1/4. b) Let dy/dx=0 and rearrange to find x=2. c) Inserting x=2 into d 2 y/dx 2 =-4x-3-1/4 will show that d 2 y/dx 2 is smaller than zero so this is a maximum stationary point. d) To find the original equation of the curve, dy/dx must be intetgrated which gives y=-2x-1-x 2 /8+c
Find the minimum value of the quadratic equation: y = x^2 + 4x - 12 To complete the square of the above equation, halve the coefficient of x (number before x) to find the value of 'a' that goes inside the bracket - this is 4 divided by 2, which is 2. To find the letter 'b', take the constant from the end of the quadratic (in this case -12) and subtract the value of a 2 from it, so b = -12 - (2*2) = -12 - 4 = -16.
Expand and simplify 3(2x + 5) – 2(x – 4) - MyTutor Expand and simplify 3(2x + 5) – 2(x – 4) Firstly, to expand an equation like this, you must multiply the brackets by the number outside of the brackets. Make sure that you multiply every number inside the bracket by the number directly outside, and remember the signs:
Draw the graph of, y = x^2 – 2x – 4 | MyTutor 1)First, let's create a table of values for x and y. For this example, let's pick values of x ranging from -2 to +4.2) We will then input our values of x into the equation, and get a corresponding value of y. We will add this to the table.
Expand and simplify (x-2)(x-4) - MyTutor One of the methods to answer this question would be the FOIL methodFirst Outer Inner LastStart by multiplying the First terms in each bracket and then the Outer and so on with Inner and Lastxx = x 2 x-4= -4x -2x= -2x and finally -4-2= 8Then you accumulate these answers x 2-4x-2x+8Next you simplify and you do this by combining the like termsIn this case you'd do -4x - 2x = -6xThe …
How do I factorise x^2 - 4? | MyTutor This is similar to other factorisation problems such as x 2 + 5x - 6. In this problem, you would find prime factors of -6 that add up to 5 (In this case -3, -2). Now, do the exact same with this problem! This is the same as x 2 + 0x - 4, so you need to find factors of -4 that add up to 0. In this case these two primes will be -2 and 2.
Simplify 4^2 x 2^4 - MyTutor 4 2 = 2 2x2 =2 4 2 4 x2 4 = 2 8 Explanation: In order to simplify powers you need to get the same base number. In order to get this problem into the simplest form you will need to use 2 as the base number. 4 is the same as 2 squared, so 4 2 is the same as 2 2x2. All you need to do now is the simplify the powers. 2 2x2 =2 4. When multiplying ...
Solve the simultaneous equations: y = x - 2 and y^2 + x^2 = 10 Curves C1 and C2 have equations y= ln(4x-7)+18 and y= a(x^2 +b)^1/2 respectively, where a and b are positive constants. The point P lies on both curves and has x-coordinate 2. It is given that the gradient of C1 at P is equal to the gradient of C2 at P.
Integrate 4/x^2 - MyTutor The graph with equation y= x^3 - 6x^2 + 11x - 6 intersects the x axis at 1, find the other 2 points at which the graph intersects the x axis Answered by Jestin J. Prove algebraically that the sum of the squares of two consecutive multiples of 5 is not a multiple of 10.
How do you factorise x^2 - 4? - MyTutor x^2 - 4 consider that in any quadratic the two numbers which end up in the brackets at the end must add up to the middle term in x. they must also multiply to make the number at the end of the quadratic termas there is no term in just x, we can put one in of 0therefore we can consider this question as x^2 + 0x - 4.Now we need to consider which ...