The function f(x) =x -x² – 2x – 1 is increasing over: %3D

Q: Let f (x) = x3 – 3x2 – 1, x 2 2. Find the value of df-1 at the point x = -1 = f (3). dx -

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Q: Find the c value satisfying MVT for f(x) = 3x² + 2 in 1 < x < 5

A: Given: fx=3x2+2 in interval 1&lt;x&lt;5

Q: s] B1(a): Find the value of k that makes function continuous at x = 4 x > 4 6x – k x < 4 3x + 6 f(x)…

A: The given function is fx=3x+6if x&gt;46x-kif x≤4. Assume that the above function is continuous at…

Q: (a) Integrate the following functions with respect to x: (i) 3x2 + 5x -7 (ii) x +

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Q: dP dt т 1- kP 1- M

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Q: Given the function g(x) = -x² + 5x +14, determine the average rate of change %3D of the function…

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Q: (d) Find the interval(s) where f(x) is decreasing.

A: There are mainly two ways roughly by which a function's behavior can be obtained and first method is…

Q: The function f:R→R defined as f(x) =log.(vv/x² +1+x+x²+1=x) is

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Q: find the diferential of the function when x = 2 and dx = 0.1 f(x) = x ln (x^3 + 2x - 4)

A: We will use the definition of differential.

Q: c. Use antidifferentiation to find f (x).

A: Since, we have asked for solving part-(c) only.Since here it is given that f'(x)=x2 ln x -(i)Here…

Q: Plot the function f(1) for -10 <xs 10. %3D 1+e5.5 – 1.5x 20

A: Graph of any function can be plotted by joining the points from which the function passes. So to…

Q: Let F(x)= ln(x^2) F'(e^4)=

A: Answer and explanation is given below...

Q: ] B1(a): Find the value of k that makes function continuous at x = 4 | 3x + 6 5х — k f(x) = x > 4 x…

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

Q: Find the domain of the function. f(x) = ln(x^2 + 1)

A: Definition used:The domain of a function is the complete set of possible values of the independent…

Q: Find the value of constant K that makes the function below continuous at x = 2. -2x X < 2 X-2 f(x)…

A: Given,           fx=x2-2xx-2 ; x&lt;2kx-3 ; x≥2

Q: Estimate the IROC for the function f(t) =Ax) = x² – 20x

A: Given: fx=x2-20x To find the instant rate of change, Differentiate the given function with respect…

Q: Find a linear approximation to f(x) = 4xe2*-6 at x = 3. Use this linear proximation to estimate the…

A: To find Linear approximation

Q: Find the family of antiderivatives for the function, f(x) = 8 12x. Which of these pass through the…

A: To find the family of antiderivatives for f(x) integrate f(x) with respect to x.

Q: Show that f(x) = ln xn /x is a decreasing function for x &gt; e and n &gt; 0.

A: Given function is, But, Hence,

Q: 3x2 Given that F(x) = In t dt, what is F'(x)? 3x 4 + t2 ||

A: Given, Fx = ∫3x3x2lnt4+t2dt  We have to find F'x.

Q: Compute d/dx f ( g (x)), where f (x) = x5, g (x) = 6x - 1

A: Given f(x)=x5, g(x)=6x-1

Q: Find the linearisation of f(x) = 4√x at a = 16. Use this to estimate 4√ 15

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Q: Differentiate. f(x) = - 2 e -X t'(x) = ]

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Q: Let L(x) be the linearization of the cube root function at x=8. When using L(x) to approximate the…

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Q: Differentiate the function In e* 8.) y = ex 7.) f(x) = e** – In :

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Q: The function fis increasing on the interval (s) (A) 0 1 © x>2 D x 2

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Q: The antiderivative of the function f(x) 5 + 10x is

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Q: Find the domain of the function g(x) = /1 – x ln x

A: We have to find domain

Q: B1(a): Find the value of k that makes function continuous at x = 4 3x + 6 x > 4 6x – k x < 4 f(x) =…

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Q: a) Let 3x2-1, for x3 f(x)= be a piecewise function. Eevaluate | Fx)dx= b) Let f(x) = 3x-1, for x< 3

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Q: Find the particular antiderivative F(x) of f(x)=4x−3 that satisfies F(1)=8.

A: The given function f(x)=4x-3, its antiderivative satisfies F(1)=8

Q: Given the function, f(x) = √x + x, use linearization at x = 4, to approximate f(4.1)

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Q: For the function f(x)=e5x+e−x defined on the interval(−∞,1], find all intervals where the function…

A: Find all the intervals for where the function is increasing and decreasing

Q: f(x) = x^3 -1000x +2022 How many local minima does this function have? are inflection points of…

A: Given function f(x)=x3-1000x+2022

Q: State the interval(s) over which the function is (a) increasing (b) decreasing (c) constant

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Q: Find E(g(X)) where g(x) = x² + x + 1. %3D

A: The E(g(X)) can be calculated as E(g(X)) = E(x2 + x + 1) = E(x2) + E(x) + 1

Q: Find f' (æ) for f (x) = 7 ln(4 + æ²).

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Q: Determine Rn(x) for f(x) = 1ln(x) about x = e

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Q: Find f''(x) for: f(x)=ln⁡x/4x

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Q: find all possible functions with the givenderivative. y' = 4x - 1/√x

A: Giveny'=4x-1x  To Find: All possible function with the above derivative

Q: Find (f1) (a). f(x) = tan-(x) 6x2, a = 0 (F-1)'(a) = Additional Materials

A: We use the property of function and inverse function and differentiate both sides with respect to x.…

Q: Find f"(0) for the function f(x) = (x+1)e².

A: Given query is to find the Indicated derivative

Q: 2. a) Find a formula for f1 for the function y = f(x) = vx – 35

A: To find f-1 for y=f(x)=√(x-35)

Q: Is f (x) = 4e-0.3xan increasing or a decreasingfunction?

A: Given: fx=4e-0.3x To Determine: Whether fx is increasing or decreasing function. Concept: a. If…

Q: Find the absolute extrema of fGx\=x. %½x°- 2 x+1 on the interval E1,2I.

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Q: Suppose ƒ is an even function and Evaluate

A: Given f is an even function, ∫-88f(x)dx=18

Q: The antiderivative of the function f(x) = .3+9x is

A: find the anti derivative (integral) of fx=56 .3+9x3

Q: n x(0)=0

A: