Question #56387

↳Redirected from "Suppose that I don't have a formula for #g(x)# but I know that #g(1) = 3# and #g'(x) = sqrt(x^2+15)# for all x. How do I use a linear approximation to estimate #g(0.9)# and #g(1.1)#?"
3 Answers
Alex C.
Jan 2, 2018

#30#

Explanation:

You can solve it with an equation like this:
#\frac{x}{6}=\frac{40}{8}#

#\frac{x}{6}=5#

#x=6*5#

#x=30#

smendyka
Jan 2, 2018

See a solution process below:

Note: Assuming you are looking for the value of "Blank"

Explanation:

We can rewrite this problem as:

#"Blank"/6 = 40/8#

Now, we can multiply each side of the equation by #color(red)(6)# to solve for #"Blank"# while keeping the equation balanced:

#color(red)(6) xx "Blank"/6 = color(red)(6) xx 40/8#

#cancel(color(red)(6)) xx "Blank"/color(red)(cancel(color(black)(6))) = 240/8#

#"Blank" = (30 xx 8)/8#

#"Blank" = (30 xx color(red)(cancel(color(black)(8))))/color(red)(cancel(color(black)(8)))#

#"Blank" = 30/1#

#"Blank" = 30#

kubik98
Jan 2, 2018

30

Explanation:

#x÷6 =40÷8#

#x/6 =40/8#

Multiply both sides by 6

#x/cancel6*cancel6 =40/8*6#

#x=40/(cancel2*4)*(cancel2*3)=40/4*3=10*3=30#

#x÷6 =40÷8=>x=30#

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