Question

Let 'f' be differentiable at c. Let y = ax + b be the equation of the tangent line to the graph of 'f' at point [c,f(c)]. Prove that

Lim F(x) - (ax + b) = 0
x->c x - c

Answer 1

whats with the x-c on the bottom there

Answer 2

Treat that limit as a fraction
i.e x -c is the denominator

Answer 3

is f and F the same function in the question

Answer 4

Ah sorry, i must have typed it up wrong ><
it's f(x) - (ax + b)

Answer 5

so u know this tangent line passes through the point c,f(c)

Answer 6

we have an indeterminate form 0/0 u can use lhopitals

Answer 7

okay

Answer 8

or split into 2 cases, when f(x) degree <1 and f(x) degree>1