I am practicing for my midterm, I would like to know if my answer is similar.(only question 2) **Problem 2.** Suppose that \( f(x) \) is a function that is continuous on the interval \([-3, 3]\). The graph of the derivative of \( f(x) \) on the interval \([-3, 3]\) is given below.**Graph Description:**The graph shown is of \( y = f'(x) \). It features several key points:- Starts at approximately \( y = 0 \) when \( x = -3 \).- Peaks at \( y = 3 \) around \( x = -2 \).- Crosses the x-axis at \( x = -1 \).- Reaches a maximum value of \( y = 4 \) at \( x = 0 \).- Falls again and crosses x-axis at \( x = 2 \) before ending at \( y = 0 \) when \( x = 3 \).**Questions:**1. Given that \( f(-1) = 2 \), find the equation of the tangent line to \( y = f(x) \) at \( x = -1 \).2. Given that \( f(1) = 9 \), evaluate the following limits, if they exist: - (a) \( \lim_{x \to 1} f(x) \) - (b) \( \lim_{x \to 1^+} f'(x) \) - (c) \( \lim_{x \to 1^-} f'(x) \) - (d) \( \lim_{x \to 1} f'(x) \)3. Does \( f'(1) \) exist? Give a brief (one-sentence) explanation.4. Does \( y = f'(x) \) satisfy the assumptions (hypothesis) of the Intermediate Value Theorem on \([-3, 3]\)? Give a brief (one-sentence) explanation.**Problem 3.** Let \( k \) be an unknown constant. Consider the function\[f(x) = \begin{cases} k^2 x - 1 & x > 1 \\ x^2 + 5 & x \leq 1 \end{cases}\]

As per the instruction, we will be answering only question 2. Given: For (a), From the given…

Answered: Problem 2. Suppose that f (x) is a…

Problem 2. Suppose that f (x) is a function that is continuous on the interval [-3, 3]. The graph of the derivative of f(x) on the interval [-3, 3] is given below.

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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