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By completing the square, find the values of x that satisfy x^4 -8x^2 +15 = 0

x^4 -8x^2 +15 = 0, we rewrite the equation in square form as (x^2-4)^2 -16 +15 =0 (x^2 -4)^2 = 1 x^2 -4 = ±1 so x^2 = 4±1, (x^2 = 3 or x^2 = 5) Therefore x = {-√3, √3, -√5, √5)
CS
Answered by Callum S. • Maths tutor
3705 Views

Find the turning point of the function y=f(x)=x^2+4x+4 and state wether it is a minimum or maximum value.

In order to find turning points, we differentiate the function. Hence we get f'(x)=2x + 4. Setting f'(x)=0 we get x = -2 and inputting this into f(x) we get y = 0 therefore the turning point is (-2,0). To fi...
BA
Answered by Basim A. • Maths tutor
13880 Views

Differentiate arctan(x) with respect to x. Leave your answer in terms of x

Let y = arctan(x). Arctan(x) is difficult to differentiate but I know how to differentiate tan(x) (=sec^2(x)) so take the tan of both sides: tan(y) = x. The next step will be to differentiate both sides. To ...
BC
Answered by Benedict C. • Maths tutor
5421 Views

Differentiate with respect to x: 3 sin^2 x + sec 2x

6 sinx cosx + (2 sin 2x)/(cos^2 2x)
HM
Answered by Hugo M. • Maths tutor
11616 Views

The functions f and g are defined on R , the set of real numbers by f(x) = x^2 - 5x +2, and g(x) = 1 - x. Find h(x) = f(g(x)), and j(x) = g(f(x)).

Part 1: Step 1: Substitute in (1-x) for x in the equation f(x) = x^2 -5x +2 Step 2: Break the brackets Step 3: Collect like terms to simplify Part2: Step 1: Substitute in (x^2 -5x +2) for x in the equation g...
DH
Answered by Daniel H. • Maths tutor
10521 Views