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f(x)=(2x+1)^0.5 for x >-0.5. Find f(12) and f'(12)

f(12)=((2 12)+1)^0.5=25^0.5=5 (simply substitute 12 into the original function)To find f'(12) we need to first find the derivative of the function and then we can substitute 12 in like we did before.f'(x)=0....
DR
Answered by Daniel R. • Maths tutor
1740 Views

Given that f(x)= (3+x^2)(x^1/2-7x). Find f'(x) (5marks)

Because there are two functions that are enclosed in brackets, you should realise that you need to differentiate by parts. You can expand out and differentiate through, but because of the x^1/2 it can get qu...
AS
Answered by Amrit S. • Maths tutor
4089 Views

What is the smallest possible value of the integral ∫(x-a)^2 dx between 0 and 1 as a varies?

This is a minimisation problem, but it's slightly tricky to see what it is we're minimising. Seeing as it's a that's varying, we are going to have to differentiate with respect to a at some point. We're goin...
RT
Answered by Ryan T. • Maths tutor
12234 Views

What is the centre and radius of the circle x^2+y^2-6x+4y=-4

First make left =0x 2 +y 2 -6x+4y+4=0Second put same terms together(x 2 -6x)+(y 2 +4y)+4=0Complete the Square (do a square (X+b) 2 that gives you you x 2 and x terms, repeat with y) these give you the centre...
FC
Answered by Flik C. • Maths tutor
3670 Views

Solve( 3x−2)/4 −(2x+5)/3= (1−x )/6

Firstly, take a common denominator for the left hand-side of the equation which would be 12 and then carrying out the subtraction. After carrying out the subtraction you will be left with two fractions - one...
WR
Answered by Wahid R. • Maths tutor
5364 Views