Determine whether f(x) =3x^2+9x-2 has a maximum of a minimum value and find that value by hand.

f(x) =3x^2+9x-2 has a minimum value. Minimum value of f(x) is

Solution:

Given, equation is

We have to find whether given equation has maximum or minimum for the given equation.

Now, we know that, f(x) is a quadratic equation and coefficient has is positive, then its graph is upward parabola. Which means that it will have minimum

The minimum value upward parabola will be its vertex.

So, let us convert f(x) into general form. That is,

where a is constant and (h, k) is vertex

Taking "3" as common from first three terms,

Now multiply and divide “2” with “3x” for easier calculations

So, by comparison with general form we get,

answer:  

step-by-step explanation:

here x represents the height of the pole,

and, the height of the shadow of the pole is 12 feet.

also, the angle of elevation from the top of the pole is 40°,

therefore,

by the low of sine,

which is the required equation for finding the value of x,