Question

The gradient at any point on the curve y=f(x) is given by the equation dy/dx=1/✓x-2.The curve passes through the point (2,3).Find the equation of this curve.​

Answer 1

Answer:

y = -1.71x + 6.42

Step-by-step explanation:

The gradient at any point on the curve is given by the expression;

$\frac{dy}{dx} = \frac{1}{\sqrt{x } - 2}$

At the point (2,3), the gradient of the curve will be:

$\frac{dy}{dx}|(x = 2) = \frac{1}{\sqrt{ 2}-2 } \\\\\frac{dy}{dx}|(x = 2) = m = - 1.71$

The equation of this curve at this point can be given by:

$y - y_1 = m(x-x_1)$

Where $x_1 =2, y_1 = 3$

Substituting these values into the given equation:

$y - 3 = -1.71(x-2)\\y - 3 = -1.71x + 3.42\\y = -1.71x + 3.42 + 3\\y = -1.71x + 6.42$