Find the maximum and minimum of g(x)= x^2-3x+4/x^2+3x+4

Step-by-step explanation:

To find the maxima/minima of a function, we solve for the derivative of the given function

Recall that according to the quotient rule of differentiation, if a function g(x) is defined as a ratio of two functions f(x) and h(x), then the derivative of g(x) is

Let

The derivative g')x) is then

Carrying out the multiplication and collecting all similar terms, we arrive at

The maxima/minima of the function g(x) occurs where g'(x) = 0 and this happens when the numerator of g'(x) is

Look at the graph above. The blue line represents the function g(x) and the red line is for the derivative of g(x) and you can clearly see that maxima/minima occurs when the red line intersects the horizontal axis, i.e., becomes zero at

d) by the cross product property, ab^2 = bc multiplied by ad

step-by-step explanation:

we are given

in the given triangle abc

angle a is 90° and segment ad is perpendicular to segment bc

we can see that

triangle(abc) and triangle(abd) are similar because they have common side and same angle (90 degree)

so, triangles(abc) and abd are similar

since, they are similar

so, the ratio of their sides must be equal

we get

now, we can cross multiply

and we get

so, this could be step to prove it

you'll just earn points here

step-by-step explanation: