Question

If the tangent line to y=f(x) at (4,3) passes through the point (0,2). Find f(4) and f'(4).

Answer 1

\(f(4)\) is given to you in the problem, since it says the tangent line at \((4,3)\)
this tells you \(f(4)=3\)

Answer 2

to find \(f'(4)\) find the slope of the line between the two points \((0,2)\) and \((4,3)\) since \(f'(4)\) is the slope

Answer 3

So the derivative of any linear function is always the slope correct?

Answer 4

the derivative gives you a formula for the slope of the tangent line
if you evaluate the derivative at a number, it gives you the slope of the line tangent at that point

Answer 5

What I meant was, the derivative evaluated at any point of a linear function is equal to the slope of the function. Is that correct?

Answer 6

@satellite73