Question

Please help. I have a calculus question about the secant of a parabola y=x^2 that passes through points A=(2,4) and A'=(2+delta x, 4+ delta y) , find the slope of this secant. I am then given a) delta x =0.01 and b) delta x = E. To answer this do I just sub in the a) and b) values of x and solve the equation?

Answer 1

hint:
the slope m of your secan t, is:
\[m = \frac{{{\delta _y}}}{{{\delta _x}}}\]

Answer 2

furthermore, we can write this:
\[\Large 4 + {\delta _y} = {\left( {2 + {\delta _x}} \right)^2}\]

Answer 3

you then solve for delta y? As values for delta x are already given?

Answer 4

from my last equation, we have:
\[\Large 4 + {\delta _y} = 4 + {\left( {{\delta _x}} \right)^2} + 4{\delta _x}\]
so we can simplify as below:
\[\Large \frac{{{\delta _y}}}{{{\delta _x}}} = {\delta _x} + 4\]

Answer 5

hmm