Question 2b 1. If f(r) = x² – 2, compute the following:a)f(1) =b)f(1+h) =c)f(1+h) – f(1)hBring your answer to the simplest possible form.2. a) Now, for the same function as above f(z) = x² – 2, compute the limitf(1+h) – f(1)limhNote: From our class discussions, recall that this limit represents in fact the value ofthe derivative of the given function at 1, i.e.f(1+h) -- f(1}f'(1) = limh-0hb) In general, what is the derivative-(x² – 2) =dzCheck your answer from a) by means of classic rules of differentiation, in other wordscompute the derivative 4 (22 – 2) at z = 1.2c) Finally, draw a large and clear sketch of the graph of f(x) = x² – 2 and illustratethe tangent line at P(1, –1). Give the slope of the tangent line at P and computethe equation of this tangent line.Note: You may want to recall that, in general, the slope of the tangent line at x = a isin fact given by the derivative of f at x = a or the instantaneous rate of change of f atx = a. As discussed in class, the instantaneous rate of change is viewed as the limit asI + a of rates of change Le-1@ Put differently, given the curve y = f(x), the slopeof the tangent line at P(a, f(a) can be interpreted as a limit of slopes of secant linesPQ as Q comes closer and closer to P along the curve, i.e.f(x) – f(a)limI- aThis limit can also be written as the limit of a difference quotient asf(a+h) – f(a).limhAs such, in our case, since a=1, we deduce that f'(1), which comes fromf'(1) = limf(x) – f(1)= limf(1+h) – f(1)I - 1hgives us nothing but the slope of the tangent line at P(1, –1). You may want to note thatwe have already computed these things in part a), and that you may just use the answer off'(1) to give the slope of the tangent line at P(1, –1).

Name: Question 2b 1. If f(r) = x² – 2, compute the following:a)f(1) =b)f(1+h
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Description: Question 2b 1. If f(r) = x² – 2, compute the following:a)f(1) =b)f(1+h) =c)f(1+h) – f(1)hBring your answer to the simplest possible form.2. a) Now, for the same function as above f(z) = x² – 2, compute the limitf(1+h) – f(1)limhNote: From our class d

Answered: b) In general, what is the derivative –…

Math

Calculus

b) In general, what is the derivative – 2) = Check your answer from a) by means of classic rules of differentiation, in other words compute the derivative (2° – 2) at z =1.

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

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