Answer:
the linearization is y = 1/4x +5/4
the linearization will produce <em>overestimates</em>
the values computed from this linearization are ...
f(3.98) ≈ 2.245
f(4.05) ≈ 2.2625
Step-by-step explanation:
Apparently, you have ...
from which you have correctly determined that ...
so that f(3) = 2 and f'(3) = 1/4. Putting these values into the point-slope form of the equation of a line, we get the linearization ...
g(x) = (1/4)(x -3) +2
g(x) = (1/4)x +5/4
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The values from this linearization will be overestimates, as the curve f(x) is concave downward everywhere. The tangent (linearization) is necessarily above the curve everywhere.
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At the given values, we find ...
g(3.98) = 2.245
g(4.05) = 2.2625
2x+2=-52
2x=-54
x=-27
That is the simple formula for it.
Answer:
The solutions are x = -4 and x = 4.
Step-by-step explanation:
Solving a quadratic equation:
We have to find x for which 
.
In this question:
So
The solutions are x = -4 and x = 4.
Answer:
Third option.
Step-by-step explanation:
You need to cube both sides of the equation. Remember the Power of a power property:
![\sqrt[3]{162x^cy^5}=3x^2y(\sqrt[3]{6y^d})\\\\(\sqrt[3]{162x^cy^5})^3=(3x^2y(\sqrt[3]{6y^d}))^3\\\\162x^cy^5=27x^6y^36y^d](https://tex.z-dn.net/?f=%5Csqrt%5B3%5D%7B162x%5Ecy%5E5%7D%3D3x%5E2y%28%5Csqrt%5B3%5D%7B6y%5Ed%7D%29%5C%5C%5C%5C%28%5Csqrt%5B3%5D%7B162x%5Ecy%5E5%7D%29%5E3%3D%283x%5E2y%28%5Csqrt%5B3%5D%7B6y%5Ed%7D%29%29%5E3%5C%5C%5C%5C162x%5Ecy%5E5%3D27x%5E6y%5E36y%5Ed)
According to the Product of powers property:
Then. simplifying you get:
Now you need to compare the exponents. You can observe that the exponent of "x" on the right side is 6, then the exponent of "x" on the left side must be 6. Therefore:
You can notice that the exponent of "y" on the left side is 5, then the exponent of "x" on the left side must be 5 too. Therefore "d" is:
Method 1.
Use 
Method 2.
Use distributive property: (a + b)(c + d) = ac + ad + bc + bd
