Use linear approximation, i.e. the tangent line, to approximate 9.2^2 as follows:
Let f(x)=x^2 and find the equation of the tangent line to f(x) at x=9. Using this, find your approximation for 9.2^2

Question

Use linear approximation, i.e. the tangent line, to approximate 9.2^2 as follows: 
Let f(x)=x^2 and find the equation of the tangent line to f(x) at x=9. Using this, find your approximation for 9.2^2

anonymous · Answer

cheat and use a calculator

anonymous · Answer

F'(x)=2x

anonymous · Answer

dy=2x dx

anonymous · Answer

i dont even know where to start or how to cheat with a calculator

anonymous · Answer

2(9)(.2)
3.6

anonymous · Answer

or find the equation of the line tangent to the graph of 
$$y=x^2$$ at the point (9,81).  the slope is 18 so the line is 
$$y=18(x-9)+81$$ now replace x by 9.2 and you get it

anonymous · Answer

ok we go slow

anonymous · Answer

81+3.6=84.6

anonymous · Answer

you want the equation of the line tangent to the graph of 
$$y=x^2$$ at the point (9,81)

anonymous · Answer

to fine the equation for the line you need two things: a point and a slope.  you already have the point.  to find the slope, take the derivative of 
$$x^2$$ which is 
$$2x$$ and replace x by 9 to get the slope of 18

anonymous · Answer

using the "point - slope" formula you know the equation for the line tangent to 
$$y=x^2$$ at (9,81) is 
$$y-81=18(x-9)$$
$$y=18(x-9)+81$$

anonymous · Answer

now replace x by 9.2 to get 
$$y=18(9-9.2)+81$$
$$y=18\times .2+81$$
$$y=3.6+81$$
$$y=84.6$$

anonymous · Answer

imranmeah way is much snappier, but maybe not so obvious.  either way

anonymous · Answer

btw 
$$9.2^2=84.64$$ so this is just an approximation.  that is what i meant when i said cheat and use a calculator.  just square 9.2

anonymous · Answer

ohh thanks a bunch man this was a great help

anonymous · Answer

yw