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A curve has equation y=x^2 + 2x +5. Find the coordinates of the point at which the gradient is equal to 1.

dy/dx= 2x+2 , gradient is equal to 1 so dy/dx also equals 1.1=2x+2-1=2xx=-1/2plug this value of x into the equation to get y=17/4
NL
Answered by Nikhil L. • Maths tutor
4178 Views

Find the derivative, dy/dx, of y = 8xcos(3x).

Let u= 8x then du/dx = 8Let v= cos(3x) then dv/dx = -3sin(3x)Therefore using the product rule: dy/dx = (cos(3x))(8) + (8x)(-3sin(3x))So dy/dx = 8cos(3x) - 24xsin(3x) .
JC
Answered by Joshua C. • Maths tutor
3923 Views

How do I tell if a curve has a maximum or a minimum?

Firstly we need to find the stationary point on the curve. We know what at a stationary point the gradient is zero so we will find the gradient of the curve. We do this by differentiation, when we have diffe...
CK
Answered by Charlotte K. • Maths tutor
7281 Views

How does integration by parts work ad when to use it?

Integration by parts should be used when you want to integrate a function composed of two factors (we can call them 'u' and 'dv'), where it is fairly easy to derive 'u', while it is difficult or impossible t...
MO
Answered by Michal O. • Maths tutor
3642 Views

A circle with centre C has equation: x^2 + y^2 + 20x - 14 y + 49 = 0. Express the circle in the form (x-a)^2 +(y-b)^2=r^2. Show that the circle touches the y-axis and crosses the x-axis in two distinct points.

Firstly we rearrange the expression to the required form:x 2 + y 2 + 20x - 14y + 49 = 0 which gives (x + 10) 2 - 100 + (y - 7) 2 - 49 + 49 = 0 and so (x - (-10)) 2 + (y -7) 2 = 10 2 Hence a = -10, b = 7 and ...
JI
Answered by John I. • Maths tutor
7951 Views