8 x 6 = 8 x(5 + [] ) = (8 x 5) + (8 x [] ) = 40 + [] = []

Mathematics

1 answer:

melisa1 [442]3 years ago

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Find the axis of symmetry and the vertex of the graph of f(x)=−6x2+24x−20

asambeis [7]

The vertex will be when the velocity is equal to zero:

df/dx=-12x+24 (using the power rule for differentiation)

df/dx=0 only when:

-12x+24=0 add 12x to both sides

12x=24 divide both sides by 12

x=2, we find the y value to be:

y(2)=-6(2^2)+24*2-20

y(2)=-24+48-20=4

So the vertex is the point (2,4)

And the axis of symmetry is the line x=2

Now if you do not yet do calculus...

The vertex will occur midway between the two zeros.

6x^2-24x+20=0 (using the Quadratic Formula for simplicity)

x=(24±√96)/12

x≈(1.1835, 2.8165)

Now the vertex occurs at the average of the zeros...

x=(1.1835+2.8165)/2=2 (as we saw earlier)

y(2)=4

Vertex is at (2,4) and axis of symmetry is the vertical line x=2

6 0

3 years ago

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Lim x->1+( sin(1-x)-(e^(x-1))+1)/ lnx

BigorU [14]

We're given the one-sided limit,

$\displaystyle\lim_{x\to1^+}\frac{\sin(1-x)-e^{x-1}+1}{\ln(x)}$

Evaluating the limand directly at <em>x</em> = 1 gives the indeterminate from

(sin(1 - 1) - exp(1 - 1) + 1) / ln(1) = 0/0

so we can potentially solve the limit by applying L'Hopital's rule. Doing so gives

$\displaystyle\lim_{x\to1^+}\frac{\sin(1-x)-e^{x-1}+1}{\ln(x)}=\lim_{x\to1^+}\frac{-\cos(1-x)-e^{x-1}}{\frac1x}=\frac{-\cos(0)-e^0}{\frac11}=\boxed{-2}$