19. Suppose f is a piecewise-defined function, equal to g(x) if x < 2 and h(x) if x > 2, where g and h are contin- uous and differentiable everywhere. If g(2) = h(2), is the function f necessarily differentiable at x = 2? Why or why not?

Q: 21. Determine the following function if continuous at 2x g(x) s6) = ; at x = 3 \x² – 4x + 3 A.…

A:

Q: 30. Consider the function defined by 0ifx 1 Sketch this graph and find all points where the graph is…

A:

Q: d) A function with no absolute extrema but with a local minimum of -5 at x = 4 and a local maximum…

A: Follow the procedure given below.

Q: 4. Is the function f(x) = (x + 1 ((x-4)² +3 ; x<4 continuous at x = 4? Why or why not? ; X24

A: Since you have asked multiple question, as per company guidelines we will solve the first question…

Q: If a continuous, differentiable function f is equal to 2 at x = 3 and at x = 5, what can you say…

A: Given f(x) is continuous and differentiable and f(3) = f(s) = 2Concept Roll's Theorem If f(x) is…

Q: Suppose that f(x) is a differentiable function and g(x)=(x+2)/f\x). If f(0)= 22 and f(0)=5, then…

A:

Q: 4 Determine if f (x) = - 2x if x 1 is differentiable at a = 1.

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Q: 1. Given the graph of f', the derivative of f, locate all extrema of f. JUSTIFY. Minimum at x =…

A: To find the minima and maxima from the graph of f'(x)

Q: 3 Show that the function f(x) = - 2x + 5x has no relative extreme points. Relative extreme points…

A: Consider the function fx=13x3−2x2+5x Differentiate fx=13x3−2x2+5x with respect to x…

Q: 9. Show that for f(x) = x° we have f"(0) = 0 but the point x = 0 is not an inflection point of f.

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Q: 5. Show that the function f(x)= 3x-9 is not differentiable at x=3. Find the formula for f'(x).

A: To Prove: Show that, given function is not differentiable at x = 3.…

Q: When a function is discontinuous at x=2, does that necessarily mean that 2 is not in the domain of…

A:

Q: S) Is the function given by 2-4x-5 f(x)= x-5 x+1,x25 .continuous at x = 5? Why or why not?

A:

Q: NOW IT'S YOUR TURN ! Find the critical points of the following functions : 1) f ( x ) = -3 x3 + x 3)…

A: f(x)=-3x13+xfirst differentiate both sides with respect to xf'(x)=-3×13x13-1+1f'(x)=-x-23+1for…

Q: On what domain is the function f(x)=1+√−6−3x continuous?

A:

Q: Find the value of k that makes function continuous at x = 4 3x + 6 x > 4 f(æ) = 6x – k x <4

A:

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

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Q: For what value of the constant c is the function f continuous on (-∞, 0)? cx2 + 8x x3 - cx if x < 5…

A:

Q: 57. Is the function given by Sx + 1, for x 4, g(x) = continuous at x = 4? Why or why not?

A: gx=12x+1,   for  x&lt;4-x+7,   for  x&gt;4 Now left hand limit at x=4 is, limx→4-fx=limx→4-12x+1…

Q: 49. Is the function given by g(x) = x² 3x continuous at x = 4? Why or why not?

A: Given: g(x)=x2-3x Determine the limit at x=4. limx→4g(x)=limx→4(x2-3x)

Q: Show that f is not differentiable at x = 1 and has a corner in its graph there. x 1

A:

Q: 5. [ 4 ifx2 Show that f(x) = is not differentiable at x = 2.

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

Q: For what value of the constant c is the function f continuous on (-∞, 0)? { cx2 + 5x if x 4

A:

Q: Where is the function f(x) = if x 0 removable discontinuity? Is it a jump discontinuity?

A: A jump discontinuity occurs when right and left limit exists but are unequal .

Q: 3) State the critical points of the function g(x) = (x – 9) 23

A: A critical point occurs when the derivative is 0 or undefined.

Q: Suppose g is the function defined by picture where k and m are constants. If g is differentiable at…

A: Solution

Q: Suppose that f(x) is a continuous function with the following values: 2 3 4 5 f(x) 2 -5| 9 5-9 1 -8…

A: Given that fx is continuous function. We draw the graph from given data

Q: 66. What will be the function g(x) resulting from normalizing the function f(x) = x³ − x4 defined in…

A: To find : function gx resulting from normalizing the function fx=x3-x4 defined in the domain 0, 34

Q: 2, if x 1

A: The given function,  f(x)=1x,if x≤1x2-1,if x&gt;1

Q: -7 if x 2. Sketch the graph of the function and use the limit definition of the derivative to show…

A:

Q: In the fucntion:  f(x)= (12-3x)(e^x)  When is the function concave up and concave down in interval…

A: Given,f(x)= (12-3x)(e^x) By definition,

Q: [4] 2. Find f'(x) using the limit definition of the derivative. Credit will not be given for any…

A:

Q: 2 Show that the function f(x) = x-4x + 10x has no relative extreme points. 3X Relative extreme…

A: Given, Function: f(x) = 23x3-4x2+10x Differentiate f(x) with respect to x, we get: f'(x) = df(x)dx…

Q: 7. Give two reasons why a function might not be differentiable at a particular value of x.

A: topic -derivative

Q: 4. Show the function f(2)=21m(z) is differentiable or not differentiable at any points.

A:

Q: 3) Find the value of k that makes function continuous at x = 4 Зх + 8 x > 4 f(x) = 4x – k x < 4 — k

A: A function is a relation from a set of inputs to a set of possible outputs where each input is…

Q: 3. Give an example of a function with discontinuities at x =1 and x = 5.

A: To Find : A function that has discontinuities at x=1 and x=5.

Q: If g is a differentiable function that g(x) less than zero for all real numbers x, and if f'(x)=…

A: To analyze the extreme values (if any) of the function f(x) under the given conditions

Q: -, Determine the location and values of the absolute maximum and absolute minimum for the given…

A:

Q: Determine all critical points for the function. f(x) = (x - 4)³

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Q: 12. Suppose we know that f (x) is continuous and differentiable on the interval [1,9], that f (9) =…

A: To find: The largest possible value of f1. Given: The fx is continuous and differentiable on the…

Q: 3. Is the function given by g(x) = x² x = 4? Why or why not? 3x continuous at

A:

Q: x+4 if x2

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Q: Suppose f is differentiable with f(0) = 0 and 0 0.

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Q: (2) Find all the points of discontinuity of the function S(x) = } x + 2 (x2 – 4 1<x< 3 x2 3

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Q: 9. Discuss the continuity of the function x 2 x2,

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Q: Suppose f(x) is a continuous function with f(-2) = 4 and f(1) = -1. What can we conclude about

A:

Q: 2. Give an example of a function f: (0, 00) → K that is continuous and bounded but does not achieve…

A: It is an usual example which derivative not vanish anywhere

Q: If f:[0, 3] → R is continuous, must its range be a closed interval?

A: If f:[0, 3] → R is continuous, must its range be a closed interval