Question

Compute the slope of the secant line between the given x-values. f(x) = x^3 - x.

a. x = 1 and x = 2
b. x = 2 and x = 3
c. x = 1.5 and x = 2
d. x = 2 and x = 2.5
e. x = 1.9 and x = 2
f. x = 2 and x = 2.1
g. Use parts a-f to estimate the slope of the tangent line at x = 2

Answer 1

@satellite73 can u help?

Answer 2

sure

Answer 3

\[f(x)=x^3-x\] so
\[f(2)=2^3-2=6\] the point \((2,6)\) is on the graph
\[f(1)=1^3-1=0\] the point \((1,0)\) is on the graph

Answer 4

the slope of the line between those two points is
\[\frac{6-0}{2-1}=6\]

Answer 5

okay got you

Answer 6

now you have a lot of questions to do, and i have to run, but the idea is the same for all of them

Answer 7

okay thanks :)

Answer 8

so for example
x = 1.9 and x = 2
you want to compute
\[\frac{f(2)-f(1.9)}{2-1.9}\]

Answer 9

i would use a calculator to compute \(f(1.9)=(1.9)^2-1.9\)

Answer 10

okay

Answer 11

1.71

Answer 12

thanks i'll do the rest

Answer 13

you get
\[\frac{6-4.959}{.1}=\frac{1.041}{.1}=10.41\] i think
check
good luck

Answer 14

ok

Answer 15

hey umm so how about g? what does it say to do?