how do you use the GRADIENT METHOD in finding the gradient of a curve????? (need answers asap!!)?

Answer 1

Hope this is fast enough.
The gradient of the curve is found using differentiation. For this method, you need to know the equation of the curve in the form of y= ax^2+bx+c (where a b and c are real numbers, can be integers or fractions) and the x values of that point which you want to find the gradient of.
If the equation is something like y=(x+2)(x+5)
expand the equation to y=x^2+7x+5 to make it easier to solve

You differentiate the individual terms of the curve i.e. ax^2 become (2)ax or 2*a*x
you keep the coefficient (the coefficient of 2x is 2), bring down the power and reduce the power by 1 (so its become 2 to 1).
Another example 4x^3 is differentiated to (3)(4)x^2 = 12x^2
_dy_
..dx denotes differentiation of the expression y (y=ax^2+bx+c) with respect to x.
The constant (c) is omitted as the power of the constant is 0 ie 5 = (5)x^0
so the equation y=ax^2+bx+c is differentiated to
_dy_
..dx = (2)ax +b (bx become be as the power of x is 1) and c is omitted.

eg. 2x^2+3x+5 is differentiated to 4x+3
Now, you sub (i.e. substitue) the value of x of the point on the curve you want the gradient for e.g. x=3 so...
_dy_
..dx = (2)ax +b becomes (2)(a)(3) +b = 6a+b

for the exmaple 2x^2+3x+5 is differentiated to 4x+3
if x=3 for the point, u sub x=3 into 4x+3 which equals to
= 4(3)+3
=15

One last example
let's say the question is to find the gradient of the curve at point G (5,7) when the equation of the curve is y=(-x+3)(x-1)
you expand the Eqn so it becomes y= -x^2 + 2x - 3
This is differentiated to -(2)x +2
You sub in the value x=5 [which is from G in the form of (x,y)]
so the gradient of point g on the curve is
-(2)(5) +2
= -10+2
=-8
Hope this is comprehensive enough, and easy to understand. I tried to give as many examples as possible.

Answer 2

differrentiate the equation of the curve . that is find the dy/dx of the equation. then substitute the given value of x.
good luck

Answer 3

If you have a function w=f(x,y,z) the gradient is
G = df/dx*i+df/dy*j +df/dz*k where df/d-are the partial derivatives of f and i,j,k the unit vectors alon the x,y and z axis respectivly

Answer 4

Just get the derivative of the curve's function!!!!

GOOD LUCK!!!