Question: Maple help

Hi!  New user here and would appreciate specifics in what to do for this lab exercise 1.  the following contains a brief intro along with exercise 1 questions.  thanks for any help!

Let f be an arbitrary continuous function defined on an interval [a − δ, a + δ] and suppose

that f has a continuous first derivative on this interval. The equation of the tangent line to

f

(1) L(x) = f (a) + f '(a)(x a).

The tangent line has many useful applications, one of which is to approximate the

function for values of x ‘near’ a. We begin by learning how to visualize approximations

to a function at a point. This is the purpose of Exercises 3.1.

Exercise 1

Question: Find the equation of the tangent line to the graph of f (x) = x + 3 at the

point (1, f (1)) . To do this: Use Maple to define an expression for f and the equation of theL. Plot both f and L on the same coordinate system. Use your Maple plot tox for which L approximates f to within 0.01. Then usex for which L approximates f to withinL approximates f to within 0.01.

 

tangent line

estimate the maximum value of

your Maple plot to estimate the minimum value of

0.01. Finally, estimate the interval over which

 

at x = a is

 

LINEAR APPROXIMATIONS:

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