Calculus four step process

Question

Use the four-step process to find the slope of the tangent line to the graph of the given function at any point. (Simplify your answers completely.)

f(x) = 4x² + 7x

Step 1: f(x + h) =

Step 2: f(x + h) − f(x) =

Step 3: (f(x+h)-f(x))/(h) =

Step 4: f '(x) = lim h→0 (f(x+h)-f(x))/(h) =

Answer 1

f'(x) = 8x +7

f(x+h) = 4(x+h)^2 +7(x+h) = 4x^2 +8xh + 4h^2 + 7x +7h = 4x^2 +15x +h^2 +7h

f(x+h)-f(x) = h^2 +8xh + 7h

f(x+h)-f(x)]/h = 8x +7 + h

as h approaches zero 8x+7+h approaches 8x +7 +0 = 8x +7