This problem concerns the piecewise-defined function f(x) given below. Here, A and P are unsp is an unspecified function with domain [95, co). Ax +4 if x<76 In(P)+7 if x = 76 x-76 f(x) = %3D if 76 95 Use this information to answer the four parts to the right.

Q: Suppose f(x)=x4+3x+1f(x)=x4+3x+1. In this problem, we will show that ff has exactly one root (or…

A: Solution Given:-         fx=x4+3x+1         Interval -5, -1

Q: 1. Find the local extrema of f(x) = x* – 2r2 +1, and state the intervals on which this function is…

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Q: 1. If the graph of f(x) = |x + 1| – 2, x -3 2x+3 c) f(x) = %3D x-1 3. If f(x) = -x² + 4x, x4 C) y=…

A: Details solution is given below:

Q: The critical points of the function f(æ) = 9x2 – 2x4 occur at x = 0, x = +1.20 0, a = +1.50 %3D %3D…

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Q: (i) Discuss the continuity of the function f(x) = {x2 − 3x    if x &lt; 2              2x + 4     if…

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Q: (i) Discuss the continuity of the function f(x)= x^2-3x        if x&lt;2…

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Q: A graphing calculator is recommended. - 1 Let f(x) = x + 1 (a) Find f'(x) and f"(x). 4x (1? + 1)?…

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Q: 2. Evaluate the piecewise function at the given values of the independent variable. 4x +4 if x < 0…

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Q: Find the local and absolute extreme values of the function on the given interval.…

A: we have to find the local and absolute extrema of f(x)

Q: Find a good numerical approximation to F(4) for the function with the properties that F′(x)=…

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Q: Find all critical points for the function f (x) 2x3 + 9x² – 60x + 9. Separate multiple answers with…

A: As we know that: To calculate the critical points, the first derivative of the given function must…

Q: In both Parts I and II of this activity, your team will be assigned one of the four groups of…

A: The vertical stretch or shrink of the graph of y=f(x) is represented by the transformation function:…

Q: Find the value of k which makes F(x) =(x+k)/(4k-1) if x&lt;=0 and F(x)= x^2+2x+k if x&gt;0 if…

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Q: For f(x) = (x2- 1) / (x + 4). Find (i) f(1)      ii) f(-x)        (iii) f(2x)

A: as per our guidelines I  am solving only first question with all three parts please resubmit other…

Q: 3. Find the local extreme points of the following function: f (x) = x3 – f(x) = x³ x² + 2x + 1

A: Differentiating with respect to x, we get Now solving the first derivative by setting it to zero,…

Q: (i) Discuss the continuity of the function f(x) = {x2²− 3x        if x &lt; 2           2x + 4…

A: We are entitled to solve one question at a time, so I am providing solution for first question.…

Q: given the function f(x)=4x^3 -5, we calculate f^-1 (x) to be

A: To find the inverse of

Q: 11. Suppose that the equation g(x, y, z) = 0 determines z as a differ- entiable function of the…

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Q: 1. Find the value of a that makes the following function differen- tiable for all x-values. Jax, if…

A: gx=ax,if x&lt;0x2-3x,if x≥0

Q: Given that f(x)=1+3x-x^2 g(x)=1-x^3 Compute f(1)

A: f(x) = 1+3x-x2 To calculate f(1)

Q: The critical number(s), if any, of the function f(x) = (x²-3x+2) is (are):

A: critical points of fx=x2-3x+2-13

Q: Find a good numerical approximation to F(4) for the function with the properties that F'(x)=…

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Q: (i) Discuss the continuity of the function f(x)={x2−3x if x&lt;22x+4 if x≥2 on the open interval…

A: Part (i):   In the region x &lt; 2 the function is defined as x2 – 3x. This polynomial is continuous…

Q: the

A: We will find the local minima, maxima, and inflection points.

Q: Find the largest interval on which the given function is increasing.

A: Consider the function fx=x-2+1 Since, fx=-x-2+1    when x&lt;2x-2+1        when x&gt;2=-x+3    when…

Q: Find the value for k so that the function will be continuous at x = -1. S 9x - 18 l-x² - 4x – 4 + k…

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Q: Determine all critical points for the following function: f(x)=12x^2+2x^3

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Q: The function given below is discontinuous at x = %3D +2x-24 f(x) = x+6

A: The solution to the given question is explained below.

Q: 10. Find function that satisfies the given conditions: f"(x)=6x³-3x+4, f'(1)=-3, f(1) = -6

A: The function satisfies the condition f''x=6x3-3x+4, f'(1)=-3, f(1)=-6 use the integration formulas,…

Q: Given f (x) = sin (z) and g (x) = x, the graph of the combined function h (x) = f (x) g (x) most…

A: Given  f(x) = sin(x) and g(x) = x

Q: If f) (E-1) and g(x) = (-1) then the function () (x) is (2z-5) %3D (2x+5) (2x-5) (2x+5) (x-1) (x-1)…

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Q: Suppose thatƒ (1) = 2, that f ' (x) is the function shown in the graph below, and that k (x) = f…

A: Equation of tangent line : y - y0  = m ( x - x0 )  m is the slope of function . And ( x0 , y0 ) is…

Q: (i) Discuss the continuity of the function f(x) = {x2 − 3x if x &lt; 22x + 4 if x ≥ 2on the open…

A: Hello. Since you have posted multiple questions and not specified which question needs to be solved,…

Q: The equation for a family of functions with zeros at +3, and -1, with end behaviors from Q2→Q4 is:…

A: “Since you have posted a question with multiple sub-parts, we will solve the first three sub-parts…

Q: Find the length L of the graph of 3 (a) f(x)=x'2 +1 for 0<x< 4 3/2 1 (b) f(x)=In x -x² for 1<x<2 8

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Q: Suppose f(1)=2 , f'(-1)=7 , g(1)=2 , g'(1)=3 Find h'(1) for h(x) = f(-x^3)

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Q: Let h(x)=f(x)g(x) where f(x)=−3x2+4x−1 and g(x)=−x2+4x+3. What is h′(4)? Do not include "h′(4)=" in…

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Q: Find a good numerical approximation to F(4) for the function with the properties that F′(x)=…

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Q: 6. If a function f satisfies f(2) = 3, and – 3< f'(x) < 3 whenever 2 < x < 5, what is the range of…

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Q: Please answer a,b,c

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Q: 2. Find the value of k so that the function defined by f(x) Sx² + 20 x 5 continuous at x = = 5.

A: We know that, a function fx is said to be continuous at x=a if and only if Left hand limit=Value of…

Q: The critical points of the function f(x) = 2x – 4x +7 is a) 1 b) 0 c) - 1 d) None of these

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Q: Find the critical points of the given function. a) f(x) = √2²-4 b) f(x) = 3x + 21-1

A: To find the critical points of the given functions.

Q: (a): Find the value of k that makes function continuous at x = 4 %3D S 2x + 8 x > 4 x < 4 f(x) = 5x…

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: If the function defined by 6x + 144 x # -24 g(x) = x + 24 k is continuous at x = -24 x = -24, then…

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Q: Find the absolute extreme values of the function on the 11) F(x) = 0.5 s x s 2 x2

A: We first find the critical values by solving F'(x)=0 F(x)=-2x2F(x)=-2x-2F'(x)=-2(-2)x-3F'(x)=4x3For…

Q: 3/11 Correct Question 3 of 6, Step 2 of 2 Consider the function: f(x) = x3 - 9x2 + 5x %3D Step 2 of…

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Q: Find the local and absolute extreme values of the function on the given interval. f(x) = x - 6x² +9x…

A: The given function is: f(x)=x3-6x2+9x+2, [2,4] Now, let…

Q: Find extreme values of the function over its natural domain. (a) f(x) = x³ + x² – 8x + 5 (b) f(x) =x…

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Q: If we apply Rolle's Theorem to the function f(x) = 2x – 12x -7 on the interval [1, 5], how many…

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