Estimate graphically the local maximum and local minimum of f(x) = 4x2 + 3x + 2

Mathematics

2 answers:

Juliette [100K]2 years ago

6 0

Hope this helps you. If you need any help regarding how to sketch graph, ping me

jarptica [38.1K]2 years ago

4 0

Seeing the graph from desmos.com, we know there is only one place where the graph will go up then down, or down then up given that the maximum exponent of x is it squared. That place, as seen, is -0.375 for the minimum as it goes down then up. There's no maximum in sight :(

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liberstina [14]

Answer:

Step-by-step explanation:

abc = 1

We have to prove that,

$\frac{1}{1+a+b^{-1}}+\frac{1}{1+b+c^{-1}}+\frac{1}{1+c+a^{-1}}=1$

We take left hand side of the given equation and solve it,

$\frac{1}{1+a+\frac{1}{b}}+\frac{1}{1+b+\frac{1}{c}}+\frac{1}{1+c+\frac{1}{a}}$

Since, abc = 1,

$\frac{1}{c}=ab$ and c = $\frac{1}{ab}$

By substituting these values in the expression,

$\frac{1}{1+a+\frac{1}{b}}+\frac{1}{1+b+\frac{1}{c}}+\frac{1}{1+c+\frac{1}{a}}=\frac{1}{1+a+\frac{1}{b}}+\frac{1}{1+b+ab}+\frac{1}{1+\frac{1}{ab}+\frac{1}{a}}$