Find the slope of the tangent (very confusing for me)

Question

Find the slope of the line to the curve at the point P

Use the formula slope of tangent = lim [x -> c] {f(x) - f(c)} / (x-c)

f(x) = (2x^2) - (7x) 3, P(c,f(c))

Answer 1

Let s = lim(x -> c) [ 2x^2 - 7x + 3 ]

Putting x = c + h, this becomes:

lim(c + h -> c) ( { [ 2(c + h)^2 - 7(c + h) + 3 ] - [ 2c^2 - 7c + 3 ] } / h )

= lim(h -> 0) {  [ 2c^2 + 4hc + 2h^2 - 7c - 7h + 3 - 2c^2 + 7c - 3 ] / h }

= lim(h -> 0) { [ 4hc + 2h^2 - 7h ] / h }

= lim(h -> 0) [ 4c - 7 ]

= 4c - 7.