If f"(x) = t"(x) for 0 < x < 1, then f(x) − t(x) for 0 < x < 1.

Q: Draw the graph of f(x) and discuss its differentiability at x = 1

A: It is given that fx=x2x≤1xx&gt;1. Recall the fact that formula for derivative of a function f at a…

Q: A function f(x) is defined as: 3 f(x) = x³-2x+ x2 At x = a, where −2 < a < 2, the tangent to the…

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Q: 3. (a) Which of the following functions have 5 in their domain? f(x) = x² - 3x *- 5 h(x) = Vx - 10…

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Q: (-3 if z 2

A: Here is a step by step solution of the problem. We have proved discontinuity at x=2 by evaluation…

Q: If f(x) In - In( + o). + e6x, find f (0).

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Q: x-²²-3 ²-3, determine the x-value(s) where f(x) changes from concave up to concave down. f(x)= Ox=…

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Q: Find the criticial numbers for f(x) = xlnx

A: Given, The function is f(x) = x lnx

Q: If f(t) = 9t+1, find f"(5). %3D

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Q: If  f′(x) < 0 for 1 <x< 6, then f is decrescent over(1,6) True or false and why

A: If  f′(x) &lt; 0 for 1 &lt;x&lt; 6, then f is decrescent over (1,6) True or false and why

Q: Identify which of the following statements are true. f(x) 7 7 (b) f'(x) True False f(x) 0 for x 7…

A: Given informationFunction f(x) with respect to x, and peak value of function at point 7 in given…

Q: If the function f(x) is defined as f(x) = = (4-2√√x)² √x -,x>0 Then, what is the value of ƒ'(16) = ?

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Q: IfY C X, show that inf (X) < inf (Y)

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Q: Consider the functions f(x)= [x²-9 x*-1 2x ; x=-1 and (3x+2 g(x) = { x=-1 Define the new function…

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Q: Let f(x) = 8 - x f-¹(x)

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Q: Compute f(x)dx 2x if x 1 f(x)

A: To find out the integration.

Q: Find an anti-derivative F(x) of f(x) = 7x³ – 6x² –- 1 satisfying that 7 F(1) = 4

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Q: Find where f(x) = 1-ax x(x-a)(x+b) is discontinuous.

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Q: If f(x)=(2/x+3) g(x)=(1/x) To Find (f o g)(x)

A: Given fx=2x+3    gx=1x

Q: The function f(x)=(1/(x+1))+4 is decreasing on what interval(s)?

A: Consider the function  fx=1x+1+4

Q: 4 Find f(x) dx if if x< 2 f(x) if x 2 2.

A: To evaluate the given integral

Q: Find f. f "(x) = 1//1- x?, () - = 2 f(x) =

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Q: If f(x) = x²/(1 + x), find f "(2). f "(2) = L

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Q: 17. Sketch the graph of f(x) = { 2x + 2, x ≤ −1 [x³−x, x>−1 and find the derivative. Determine…

A: 17. Sketch the graph of  and find the derivative.Determine whether  satisfies the conditions of the…

Q: Express the function in the form fog. (i) F(x) = (2r + r*)ª. (ii) F(r) = %3D 1+ VE

A: Answer