# calculus totally confused

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find a first degree polynomial function p(1) whose value and slope agree with the value and slope of f at x=c. i think you use taylor series for this

f(x)=4/sqrt(x), c=1

i'm totally confused on how to do it. i know you find the derivative but how do i get the function. this is number five on my homework so if you help me on this, i will be able to do the rest.

A first degree polynomial is a straight line of the form y = mx + b.
They are asking you for the equation of a line tangent to 4/sqrt(x) = 4 x^-(1/2) at x = 1
The value of y=f(x) at that point is y = 4
The value of the slope is
dy/dx = -2x^(-3/2), and when x=1, that slope is -2.
The equation of the tangent line is
(y-4)/(x-1) = -2
Convert that to y = mx + b form.
y-4 = -2x + 2
y = -2x + 6

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