7) Find the value of k that makes the function continuous. Is the function differentiable at x = 2 for this value of k? Justify your answers. [4х - 3, х<2 f (x) = x? +k, x> 2

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Q: 2. Given the function: f(x) 3 x -3 x≤2 2 x² + 1 x > 2 Is f(x) continuous and differentiable at x=2?

A: Here is the solution:

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Q: 2) Consider the function g(x) = x³ + 3x2 - 9x + 2 on the interval [-4,2]. Find all local extrema,…

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Q: ecos-1 x if x 1

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Q: 2) An elastic tire is described by the iven by the function f(x, y) = 4xy. Use

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Q: Q3) if the continuous function is : 4x+1 F(x) -+k at x= h. Find the value of h,k.

A: 3). Given function is:   fx=4x+1x&lt;hx3+kx=hx2+1x&gt;h Solution: A function fx is continuous at x=h…

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Q: 4). If f(1) = 12 and f' is continuous and | f'(x) dx=17, what is the value of f(4)?

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Q: 4). If f(1) = 12 and f' is continuous and f'(x) dx=17, what is the value of f(4)?

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Q: 25. Use the definition of differentiability to prove that the following function is differentiable…

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Q: 1) Find the absolute extremum values of f(x) = x2 – 4x + 18 over the interval [1, 4]. [2 marks]

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Q: 1. Can Rolle's Theorem be applied to y = (x – 2)3 on the interval [0, 4]? Justify.

A: Check differentiability at x=2

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A: use double differentiation =0 to find inflection points and concavity

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Q: 2- Calculate the extremum point of below function and Classify it f(x) = 4 x3 + 2 v11 – x + x?

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Q: Find the value of k that makes function continuous at I = 4 2x + 8 x > 4 f(x) = 4x k r< 4

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Q: Is the function F(x) as given is constant, increasing, or decreasing on the interval (0, ∞)?…

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Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.