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Calculate the gradient of the function y=x^2+6x when y=-9

-9=x^2+6x 0=x^2+6x+9 0=(x+3)(x+3) when y=-9 x=3 dy/dx=2x+6 dy/dx=2(3)+6=12
HM
Answered by Hassan M. • Maths tutor
5509 Views

For a curve of gradient dy/dx = (2/(x^2))-x/4, determine a) d^2y/dx^2 b) the stationary point where y=5/2 c) whether this is a maximum or minmum point and d) the equation of the curve

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 sta...
KM
Answered by Katie M. • Maths tutor
6141 Views

Find ∫ ( 2x^4 - 4x^(-0.5) + 3 ) dx

When integrating, you need to add one to the power and divide the term by the power. We will consider each term individually, 2x 4 will become (2x 4+1 )/(4+1) = (2x 5 )/5, -4x -0.5 will become (-4x -0.5+1 )/...
RM
Answered by Rebecca M. • Maths tutor
7450 Views

A curve has equation y = f(x) and passes through the point (4,22). Given that f'(x) = 3x^2 - 3x^(1/2) - 7 use intergration to find f(x).

As f '(x) is the differential of f(x) we have to first integrate f '(x). To do this we take each term individually and integrate it. So starting with 3x 2 , to integrate a simple function of x like this we h...
JO
Answered by Jonathan O. • Maths tutor
8262 Views

how do you do binomial expansion when the power is a negative

There is a simple equation, similar to the normal binomial expansion, thats easy to remember once youve used it a few times. (1+x) n =1+nx+{[n(n-1)]/2!}x 2 +{[n(n-1)(n-2)]/3!}x 3 +... This looks complicated ...
SM
Answered by Sarah M. • Maths tutor
11102 Views