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Brilliant_brown [7]
3 years ago
14

Use the lim f(x)-f(a)/x-a to find the derivative.

Mathematics
1 answer:
Tresset [83]3 years ago
4 0
Hello,

f(x)-f(a)= -3x²-5x+1-(-3a²-5a+1)=-3(x²-a²)-5(x-a)=-3(x-a)(x+a)-5(x-a)
=-(x-a)(3(x+a)+5)
=-(x-a)(3x+3a+5)

lim (f(x)-f(a))/(x-a)=- lim (3x+3a+5)=3a+3a+5=-6a-5
if a=1==>-6*1-5=-11

Otherwise
f'(x)=-6x-5
f'(1)=-6-5=-11



at point(1,-7)

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consider the graph of the following qudratic equation. y= -x^2 -10x + 24.What is the y-value of the vertex?
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Given that the quadratic equation is y=-x^{2}-10 x+24

We need to determine the y - value of the vertex.

<u>The x - value of the vertex:</u>

The x - value of the vertex can be determined using the formula,

x=-\frac{b}{2 a}

where a=-1, b=-10, c=24

Substituting these values, we get;

x=-\frac{(-10)}{2(-1)}

Simplifying the terms, we get;

x=-\frac{-10}{-2}

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Thus, the x - value of the vertex is -5.

<u>The y - value of the vertex:</u>

The y - value of the vertex can be determined by substituting the x - value of the vertex ( x = -5) in the equation y=-x^{2}-10 x+24

Thus, we get;

y=-(-5)^{2}-10(-5)+24

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Thus, the y - value of the vertex is 49.

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