Slope of the tangent using limit

Question

Use the limit definition of the derivative to find the slope of the tangent line to the curve  at 

Answer 1

f'(x) = slope of tangent line at the point (x, f(x))

f'(x) = lim_h→0 [(f(x+h) - f(x)) / h] = lim_h→0 [(6(x+h)² +4(x+h) + 5 - (6x² + 4x + 5))/h] =

lim_h→0 [(12xh +6h² + 4h)/h] = lim_h→0 [h(12x + 6h + 4) / h] = lim_h→0(12x + 6h + 4) = 12x + 4

So, f'(1) = 16.