Question

Find the equation of the tangent line to the graph f(x)=x^2-2at x=xnaught

Answer 1

can you find the derivative of f(x) with respect to x ?
the derivative will be a function that defines the slope of the tangent line at any given x

Evaluate f'(x) at \( x_0 \) to get m, the slope of the tangent line.
Evaluate f(x) at \( x_0 \) to get \( y_0 \)

Once you have slope m and a point on the line \( ( x_0, y_0) \), you can find the equation of the line using
\[ y - y_0 = m(x-x_0) \]

Answer 2

y=x^2 - 2
dy/dx = 2x
You know the equation of the line when a point and slope are given:
y-yo = m(x-xo)
Plugging in the value, we get
y-xo^2 - 2 = 2xo(x-xo)
y = 2xo*x - (xo^2+2)
The above equation is in y = mx+c form.