Using the definition of the derivative, find f'(x) for the following function.3. f(x) = x2 – 3x + 8%3Dthe definition of the derivativef(x + h) – f(x)f'(x) = limh-0hWhat is the slope of tangent line to this curve at x = 1?

Here We have to use the definition of the derivative.

Answered: Using the definition of the derivative,…

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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Please assist with the steps below Find the derivative of the function by using the rules of differentiation. F(x)=0.003x^3-.04x^2+.1x-29
The temperature in an industrial pasteurization tank is f(x)= x2 − 9x + 111 degrees centigrade after x minutes (for 0 ≤ x ≤ 11). (a) Find f '(x) by using the definition of the derivative._________ b) Use your answer to part(a) to find the instantaneous rate of change of the temperature after 3 minutes. Be sure to interpret the sign of your answer. The temperature is increasing or decreasing at a rate of ________degrees per minutes after 3 minutes. c) Use your anser to part (a) to find the instantanrous rate of change after 8 minutes. The temperature is increasing or decreasing at a rate of ______ degrees per minute after 8 minutes.
The derivative of a function is f '(x) = x²(x + 4). At what value(s) of x does f have a horizontal tangent line? Explain. %3D If f(1) = -3, find the equation of the tangent line to f at x = 1. %3D
F(x) = 18/x Use the following formula to find the derivative of the function (F(t) - f(x))/(t-x) What is the tangent line of the function when x = 6?

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Using the definition of the derivative, find f'(x) for the following function. 3. f(x) = x² – 3x + 8 %3D - the definition of the derivative f(x + h) – f(x) f'(x) = lim h-0 h What is the slope of tangent line to this curve at x = 1?