Question

From first principles (ie using the tangent slope method), find the slope of the following curves at the given value of x.

f(x)=2x^2− 6x at x = 3

Answer 1

f(3) = 2(9) - 6(3) = 0

f(3+h) = 2(3+h)^2 - 6(3+h)
= 2(9 + 6h + h^2 - 18 - 6h
= 2h^2 + 6h

slope = lim (f(3+h) - f(3) )/h , as h--->0
= lim(2h^2 + 6h - 0)/h
= lim h(2h + 6)/h
= lim 2h + 6 , as h ---> 0
= 6