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Solve the inequality 􏰂|2x + 1|􏰂 < 3|􏰂x − 2|􏰂.

(2x+1) 2 &lt; 9(x-2) 2 4x 2 +4x+1 &lt; 9(x 2 -4x+4)4x 2 +4x+1 &lt; 9x 2 -36x+360 &lt; 5x 2 -40x+35Apply quadratic equation solving formula (40+30)/10=7 and (40-30)/10=1hence x&lt;1 and x&gt;7
AT
Answered by Alejandra T. • Maths tutor
9997 Views

The curve C has equation y=3x^3-11x+1/2. The point P has coordinates (1, 3) and lies on C . Find the equation of the tangent to C at P.

In order to find the gradient of a tangent to the curve C we must differentiate our equation for C.dy/dx= 9x 2 -11To find the gradient of a tangent at a specific point P we substitute the coordinates of P in...
CW
Answered by Chloe W. • Maths tutor
6229 Views

Complete the square of 2x^2+16x-24 and hence state the minimum value of the function

2[(x^2+8x-12) [Explain basic complete the square technique]2[(x+4)^2 -16 -12]2[(x+4)^2-28]2(x+4)^2-56The term (x+4)^2 is always greater or equal to 0. So the smallest value it can have is 0. So the minimum v...
JS
Answered by Jake S. • Maths tutor
4533 Views

f(x) = (x-5)/(x^2+5x+4), express this in partial fractions and hence find the integral of f(x) dx between x=0 and x=2, giving the answer as a single simplified logarithm.

f(x) = (x - 5) / (x + 4)(x + 1) let f(x) = A / (x + 4) + B / (x + 1) so (x - 5) / (x + 4)(x + 1) = A / (x + 4) + B / (x + 1) then multiplying by (x+4)(x+1), we get x - 5 = A(x + 1) + B(x + 4) x - 5 = Ax + A ...
TS
Answered by Toby S. • Maths tutor
4198 Views

Is the function f(x)=x^3+24x+3 an increasing or decreasing function?

f(x)=x^3 +24x+3 f'(x)=3x2+24 Since x^2&gt;0 for all real x 3x^2+24&gt;0 So f(x) is an increasing function
DM
Answered by Danni M. • Maths tutor
4776 Views