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Art [367]
2 years ago
11

(1/4) to the -4 power

Mathematics
1 answer:
GalinKa [24]2 years ago
5 0
The answer would be -1/32 i think.
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Math- Differentiation . Could you help me to solve this question?
Arlecino [84]

Answer:

Step-by-step explanation:

Hello, first of all we can find a value for f(1)

xf(x)+f(x^2)=2 \\\\\text{So for x = 1, it gives}\\\\f(1)+f(1^2)=f(1)+f(1)=2f(1)=2\\\\ f(1) =1

And we can get the derivative of the equation so.

(uv)'=u'v+uv' \text{ and } \dfrac{df(x^2)}{dx}=2xf'(x^2) \text{ so we can write}\\\\f(x)+xf'(x)+2xf'(x^2)=0\\\\\text{And then, for x = 1}\\\\f(1)+f'(1)+2f'(1)=0\\\\ f(1)+3f'(1)=0\\\\ 3f'(1)=-f(1)=-1\\\\\large \boxed{ f'(1)=-\dfrac{1}{3} }

Thank you

4 0
2 years ago
Help PLEASE<br> I need help rn plsssssss I beg youu
olasank [31]
Rectangular prism Area=2(wl+hl+hw) in this case, the length (l) is 9m, the width (w) is 8m, the height (h) is 9m. Just plug everything into the formula: 2(8*9+9*9+9*8)=450m^3. Hopefully It helped. Have a good day.
3 0
2 years ago
Read 2 more answers
4.
S_A_V [24]

Answer:

Answer is the 72.02 cm³ .I hope it's helpful to you.

5 0
3 years ago
How do you find the lateral area of a pentagonal prism?
Sloan [31]
AL=5ah!!!!!!!!!! Hope it helps
3 0
2 years ago
Graph the function and analyze it for domain, range, continuity, increasing or decreaseing behavior, symmetry, boundedness, extr
Sunny_sXe [5.5K]

Answer:

f(x) = 3 \cdot 0.2^x

Step-by-step explanation:

f(x) = 3 \cdot 0.2^x


Domain of f: "What values of x can we plug into this equation?" This makes sense for all real numbers so the domain is \mathbb{R}

Range of f: "What values of f(x) can we get out of the function?" From the graph we see we can get any real number greater than 0 out of the function by choosing a suitable x-value in the domain. The range is therefore (0, \infty).

Continuity: Since the graph is one, unbroken curve (i.e. a curve that can be drawn in one movement without taking your pen off the paper). We see that "roughly speaking" the function is continuous.

Increasing or decreasing behaviour: For all x in the domain, as x increases, f(x) decreases. This means the function exhibits decreasing behaviour.

Symmetry: It is clear to see the graph of f(x) has no symmetry.

Boundedness: Looking at the graph we see it is unbounded above as when we choose negative values, the graph of f(x) explodes upwards exponentially. Choose a value of x, plug it in, next choose (x-1), plug this in and we observe f(x-1) > f(x) for all x in the domain.

The function is however bounded below by 0: no value of x in the domain exists which satisfies f(x) < 0.

Extrema: As far as I can tell, there are no turning points on the curve. (Is this what you mean by extrema?)

Asymptotes: Contrary to the curve's appearance, there are no vertical asymtotes for this curve. The negative-x portion of the curve is just growing so quickly it appears to look like an asymptote. There is a value of f(x) for all x<0. There is however a horizontal asymtote: y=0.

End behaviour: As x \rightarrow \infty, f(x) \rightarrow 0. As x \rightarrow -\infty, f(x) \rightarrow +\infty

5 0
3 years ago
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