Question

Help? I have a few calculus questions that i need help with.

Answer 1

just post the specifics

Answer 2

Use a tangent line approximation with the function\[g(x)=\sqrt{x}\]to estimate \[\sqrt{9.2}\]

Answer 3

I think they want you to use this formula:
\[ f(x) \approx g(x_0) + g'(x_0)(x - x_0)\]
where \[g(x) = x^{\frac{1}{2}} \]
and \(x_0=9\)

Answer 4

?

Answer 5

If that does not make sense, it comes from the first two terms of a taylor series
https://www.khanacademy.org/math/calculus/sequences_series_approx_calc/old_maclaurin_series/v/polynomial-approximation-of-functions--part-1

Answer 6

how dp i get the derivative of 9.2^1/2?

Answer 7

The idea is to find the equation of the tangent line, at the point (9,3)
the slope of the tangent line is dy/dx evaluated at (9,3)
in other words, with \[ y = x^{\frac{1}{3}} \]
find dy/dx , and find its value when x = 9
you now know the slope m and a point on the line.
Use the point- slope formula
y - y0 = m(x-x0) where (x0,y0) is the point (9,3)
y - 3 = m(x -9)
or
y = 3 + m(x-9)
if you plug in x= 9.2, you will get a y that is approximately the square root of y
see this graph: