Question
find the slope of the tangent line to the parabola y=x^2+3x at the point (-1, -2)
using lim x-->a (f(x)-f(a))/x-a
using lim x-->a (f(x)-f(a))/x-a
Answers
oobleck
just plug in your function
f(x)-f(a) = (x^2+3x)-(a^2+3a) = (x^2-a^2) + 3(x-a)
= (x+a)(x-a)+3(x-a) = (x-a)/(x+a+3)
so (f(x)-f(a)/(x-a) = x+a+3 for any value x≠a
Now take the limit as x→a
f(x)-f(a) = (x^2+3x)-(a^2+3a) = (x^2-a^2) + 3(x-a)
= (x+a)(x-a)+3(x-a) = (x-a)/(x+a+3)
so (f(x)-f(a)/(x-a) = x+a+3 for any value x≠a
Now take the limit as x→a