Solving General Curve y=kx^n Tangent at P(a,kan)

[ProgMetal]

Homework Statement

Consider now the point P(a, kaⁿ) on the general curve y=kxⁿ. where n is any non zero real number and k >0.

find the equation of the tangent at the point P
find coordinates of the points A and B where the tangent meets the x-axis and y-axis respectively.

Homework Equations

The Attempt at a Solution

I have what should be the gradient of the tangent, simply the derivative of y=kxⁿ (dy/dx=knx^n-1). but i am unsure as finding the x and y intercepts is proving difficult. Should the highest power of x be 1 as the tangent should be linear, thus making the tangent simply y=kx? or is there something more...

 

[rock.freak667]

The Attempt at a Solution

I have what should be the gradient of the tangent, simply the derivative of y=kxⁿ (dy/dx=knx^n-1). but i am unsure as finding the x and y intercepts is proving difficult. Should the highest power of x be 1 as the tangent should be linear, thus making the tangent simply y=kx? or is there something more...

You would need to get the gradient at point P, which is just dy/dx at x=a. (This will be 'm')

Then just use the formula for find a line given a point and the gradient.

(y-y₀)/(x-x₀) = m