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Express x^2 + 5x + 10 in the form (x+p)^2 +q

x^2+5x+10 -> (x+p)^2+q (x+5/2)^2 - (5/2)^2 + 10 (x+5/2)^2 - (25/4) +40/4 (x+5/2)^2 +15/4
IB
Answered by Imogene B. • Maths tutor
6437 Views

Given that y = 4x^3 – 5/(x^2) , x not equal to 0, find in their simplest form (a) dy/dx, and (b) integral of y with respect to x.

a) When differentiating y, the method with each term is to 'times by the power and minus 1'. In order to apply this, we need every term to consist of a coefficient multiplied by a power of x. To start with w...
IA
Answered by Izzy A. • Maths tutor
9924 Views

Integral of sin^x dx

Use double angle formula to rearrange for cos2x this gives: x/2 + 1/4sin2x + C (constant)
MB
Answered by Martin B. • Maths tutor
5060 Views

give the coordinates of the stationary points of the curve y = x^4 - 4x^3 + 27 and state with reason if they are minumum, maximum, or points of inflection.

differentiating the equation gives dy/dx = 4x^3 - 12x^2 dy/dx = 4x^2(x - 3) at a turning point, dy/dx = 0. Solving the equation 4x^2(x - 3) = 0 yeilds x = 0, x = 3 putting 0 and 3 back into the curves equati...
MB
Answered by Matthew B. • Maths tutor
12940 Views

How to find the stationary point of y= x^2-108x^(1/2)+16 and determine the nature of the stationary point?

a). Find stationary point: Stationary point is the point at which the gradient equals zero. So first we must find the gradient and the set it to zero and solve: dy/dx= 2x-54x^(-1/2); now we set this to zero:...
DS
Answered by Dylan S. • Maths tutor
5511 Views