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denpristay [2]
2 years ago
6

Let f(x) = 5x − 6. Simplify each of the following expressions.

Mathematics
1 answer:
patriot [66]2 years ago
4 0

Answer:

Explanation:

in each of the following substitute x with the variables in the bracket.

f(a) = 5x - 6

= 5a - 6

f(a+h) = 5 (a + h) - 6

= 5a + 5h - 6

f(a+h) - f(a) = (5a + 5h - 6) - (5a - 6)

= 5a + 5h - 6 - 5a + 6

= 5h

(as the 5a's and 6's cancel each other out.)

f(a+h) - f(a)/h = 5a + 5h - 6 - ((5a - 6)÷h)

take l.c.m

= <u>(5ah + 5h^2 - 6h - 5a + 6)</u>

h

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geniusboy [140]
<span>3x – 15y = 60

y-intercept x = 0</span>
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How to solve these question?
mart [117]
3.) An extreme value refers to a point on the graph that is possibly a maximum or minimum. At these points, the instantaneous rate of change (slope) of the  graph is 0 because the line tangent to the point is horizontal. We can find the rate of change  by taking the derivative of the function.

y' = 2ax + b

Now that we where the derivative, we can set it equal to 0.

2ax + b = 0

We also know that at the extreme value, x = -1/2. We can plug that in as well.

2a (-\frac{1}{2} ) + b = 0

The 2 and one-half cancel each other out.

-a + b = 0

a = b

Now we know that a and b are the same number, and that ax^2 + bx + 10 = 0 at x = -1/2. So let's plug -1/2 in for x in the original function, and solve for a/b.

a(-0.5)^2 + a(-0.5) + 10 = 0

0.25a - 0.5a + 10 = 0

-0.25a = -10

a = 40

b = 40

To determine if the extrema is a minima or maxima, we need to go back to the derivative and plug in a/b.

80x + 40

Our critical number is x = -1/2. We need to plug a number that is less than -1/2  and a number that is greater than -1/2 into the derivative.

LESS THAN:
80(-1) + 40 =  -40

GREATER THAN:
80(0) + 40 = 40

The rate of change of the graph changes from negative  to positive at x = -1/2, therefore the extreme value is a minimum.

4.) If the quadratic function is symmetrical about x = 3, that means that the minimum or maximum must be at x = 3.

y' = 2ax + 1

2a(3) + 1 = 0

6a = -1

a = -1/6

So now plug the a value and x=3 into the original function to find the extreme value.

(-1/6)(3)^2 + 3 + 3 = 4.5

The extreme value is 4.5


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