Determine where the function f ( x ) f\left(x\right) f ( x ) is not differentiable. f ( x ) = 3 x + 2 f\left(x\right)=\frac{3}{x+2} f ( x ) = x + 2 3

in this problem, we are given the function f of x is equal to 3 over x plus 2, and we're asked to determine where the function f of x is not differentiable. Now, whenever we're trying to figure out where something is not differentiable, a good place to start is to first see whether or not the function is continuous for all x values. Now I see that we have this function right here, which is a rational function. And one of the things that I know is that there is a domain restriction for rational functions. The denominator cannot be equal to 0, the bottom of the fraction. Because whenever this bottom of the fraction is 0, that means we'd be dividing by 0, and that's something we cannot do in math. So we can say that x plus 2 cannot equal 0, and what we can do is solve this inequality for x. So I'm gonna go ahead and subtract 2 on both sides here, and that will get the 2's to cancel right over there, leaving me with x cannot equal negative 2. So this right here is a place where the function would break if we try to plug in negative 2 for x. And if we do that, we would actually end up having an asymptote in our graph. And recall that a function is not continuous whenever you have a junk, a hole, or an asymptote, which is a place where the function cannot exist. So in this case, we would say that at x equals negative 2, our function here is not continuous. And because it's not continuous, by default, it's not going to be differentiable at x equals negative 2. So this right here would be the solution, and that is where the function is not differentiable. So hope you found this video helpful. Let's go ahead and get some more practice.

2. Intro to Derivatives

Differentiability

Calculus

2. Intro to Derivatives

Differentiability

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Multiple Choice

Determine where the function $f$\left$(x$\right$)$ is not differentiable.
$f$\left$(x$\right$)=$\frac{3}{x+2}$$

-2

Verified step by step guidance

Identify the function given: $ f(x) = \frac{3}{x+2} $. This is a rational function, which is typically differentiable except where the denominator is zero.

Set the denominator equal to zero to find points of non-differentiability: $ x + 2 = 0 $.

Solve the equation $ x + 2 = 0 $ to find the value of $ x $ where the function is not differentiable.

The solution to $ x + 2 = 0 $ is $ x = -2 $. This is the point where the function is not differentiable because the denominator becomes zero, leading to a division by zero.

Conclude that the function $ f(x) = \frac{3}{x+2} $ is not differentiable at $ x = -2 $.

5:02m

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Struggling with Calculus?

Determine where the function f(x)f\(\left\)(x\(\right\))f(x) is not differentiable.f(x)=3x+2f\(\left\)(x\(\right\))=\(\frac{3}{x+2}\)f(x)=x+23

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Differentiability practice set

Determine where the function $f\(\left\)(x\(\right\))$ is not differentiable.
$f\(\left\)(x\(\right\))=\(\frac{3}{x+2}\)$