Each of question gives the first derivative of a continuous functiony = ƒ(x). Find y'' and then use Steps 2–4 of the graphing procedureto sketch the general shape of the graph of ƒ. y' = x2 - x - 6

Q: Find f-1 if f (z) = iz + 1.

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Q: Find the first derivative: y = In V2x3-5 Oý = 203-5 O y = 4x2 203-5 3x2 O Ý = 23-5 O Ý = 6 52 y =…

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Q: 8. State the location of the x intercepts of the function y = sinx and the vertical asymptotes of…

A: We need to determine the x-intercepts of the function y=sin x and vertical asymptotes of the…

Q: 4. y = (8x*- 5x2 + 1)* 5. g(t) = -3V7t3 – 1

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Q: Use the definition of the derivative to find the equations of the lines described in Exercises…

A: We can use the definition of derivatives to find the equation of tangent line at any point on curve…

Q: - For the following graphical representation of a function f(x): (1) Mark the points on the graph…

A: Since you have posted a question with multiple subparts, so we will solve only the first three…

Q: Set f(x) = 1 7x³ + 3x + 2 . (1, 1/12) is on the graph of ƒ. Find (ƒ-²¹) (¹2). The point 1,

A: The solution to find the value of inverse of f(x) at 1/12 is as follow.

Q: 1. What is chain rule differentiation?

A: Query- What is chain rule differentiation? Answer- Chain rule differentiation is the rule to find…

Q: Show that ⊢ (x > 0) y = x + 1 (y > 1)

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Q: Use the guidelines from section 4.5 to graph the function f(x) = x2/3 (6 – x)/3 For your…

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Q: Match the graph of each function in (a)–(d) with the graph of its derivative in I-IV. Give reasons…

A: (a) Observe from the graph that the tangents are horizontal at two points. That means f'(x) has two…

Q: Vt- 4 V3t - 4 y =

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Q: Find the derivatives of the functions in Exercis y = (1 + 2x)e-2x

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Q: 6) Use derivatives to find where the function is concave up f(x)=x.e2x*

A: If  f "(x) > 0  on an interval, then f(x) is concave up on that interval.

Q: Find the x-coordinates of all of the points on the graph of f (x) where the derivative equals 0.…

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Q: Differentiate. f(x) = In In dx (5x + 2)(x+7)3 (1-6x)6 (5x+2)(x+7)3 (1-6x)6

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Q: Prob. 6 (a) i) Let f(x) = 2x² - 3. Find f'(-2) using only the limit definition of derivatives. (b)…

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Q: given the following information about its derivative: f'(x) -2 f'(x) = 0 at x = -2 -10

A: We will use relation between derivative  and character of the graph to draw

Q: 2) Use the Chain Rule to express the second derivative of fog in terms of the first and second…

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Q: √x √x + √√y = 1

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Q: Use derivatives to sketch the graph of f(x) = (x² – 8x + 16)e².

A: Given

Q: Match each function to the rule you would need to use to compute its derivative. Answers may be used…

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Q: 8) Find the derivative of the function f(x) = (2x-1 x² + 1 if x ≤0 if x>0

A: Step 1:   Step 2: Step 3: Step 4:

Q: Sketch a function where ?′(?) > 0  and ?′′(?) > 0 always and passes through the point (0,1).

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Q: Find f. f"(x)  =x6 - 4x4 +x +1

A: ∫xndx = xn+1n+1+C