Find f(x+h)-f(x)/h

Question

f(x)=-7x²+4x-5

Answer 1

f(x) = 7x^2 +4x -5

f(x+h) = 7(x+h)^2 +4(x+h) -5 = 7(x^2 -2xh + h^2) + 4x +4h -5 = 7x^2 -14xh +h^2 +4x +4h -5

f(x+h) - f(x) = 14xh +4h +h^2

(f(x+h) -f(x))/h = 14x +4 + h

which also = derivative of f(x) +h = f'(x) +h

which also = the slope of the secant line connecting (x, f(x) to (x+h, f(x+h))

which approaches slope of the tangent line when h approaches zero at the point (x,f(x))