Let ƒ be the function given by ƒ(x) = (x-2)²(x+3). For what values of x is f not continuous?

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Q: determine at which points, the function f(x)=x2 if x∈Q if x and f(x)=-x2 if x∈R/Q is continuous.

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A: topic - limits and continuity

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A: Given         f(x) =|x-3|

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Q: what is the mathematical condition for the function to be continuous at a certain point c?  is the…

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A: Product Rule of differentiation : d(u.v)dx = u.dvdx + dudx.v

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Q: Let f(x)=x^3-4x^2. Find the points on the graph of f where the tangent line is horizontal.

A: f(x) = x3 - 4x2Horizontal tangent when f'(x) = 0differentiate f(x) with respect to 'x'f'(x) = 3x2 -…

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Q: Examine whether or not the function (4-x² f (x) =- [4+x if x0 Is continuous at x = 0

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Q: Find the value of the constant ( a, b, or c) that makes the function continuous.

A: Given: fx=1x,x&lt;-1, x&gt;12ax+b,-1≤x≤12 if given function is continuous then limx→-1-fx=limx→-1+fx…

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A: Given that: f(x)=x33-x22-6x

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Q: What is f'(x) at x = -1 of the function f(x)=x^-2 + (x^2)^(1/2) *

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Q: If f(x) is a function that is defined for all x E R, then f(ƒ-'(x)) = = x. True

A: Let,  f(x) = a*x+b f-1(x) = (x-b)/a

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Q: Determine if the function is continuous at the given point. 1 f(x) = {* - (x2 – 2 x 0 at x = 0.

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Q: (c) Determine whether f (x) is continuous at x-2, where [4x+3, xs2 f(x)= 8-x, x2

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A: Now differentiating f(x) with respect to x, we get Now,

Q: ) Use the Intermediate Value Theorem to show that there is one such that f"(a) = 0. point x = a

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Q: Draw a function F(x), defined for all real numbers x, that satisfies the following properties.…

A: The first derivative is everywhere positive and the second derivative is everywhere negative

Rate of Change

The relation between two quantities which displays how much greater one quantity is than another is called ratio.

Slope

The change in the vertical distances is known as the rise and the change in the horizontal distances is known as the run. So, the rise divided by run is nothing but a slope value. It is calculated with simple algebraic equations as: