Question

Find f(3) and f'(3), assuming that the tangent line to y=f(x) at a=3 has the equation y=5x+2

Answer 1

`y=5x+2=5x-15+15+2=5(x-3)+17\implies y-17=5(x-3)`

The tangent line to
`f(x)` at
`x=c`, given the slope
`f'(c)` at
`x=c`, is


`y-f(c)=f'(c)(x-c)`

In this case,
`c=3`. Matching this with the equation above, you find that
`f(c)=17` and
`f'(c)=5`.