Question

How do you find the maximum or minimum of `f(x)=3/4x^2-5x-2`?

Answer 1

I tried this:

Explanation:

This is a Quadratic Function that is represented by a Parabola. Due to the positive coefficient of `x^2` the parabola will have the concavity similar to a letter U, having only a minimum.

To find the coordinates of the minimum you can derive the function:
`f'(x)=3/2x-5`
and set this equal to zero:
`3/2x-5=0`
solve it:
`x=5*2/3=10/3`
substitute this into your original function to get the `y` value of your minimum.

Graphically:
graph{(3/4)x^2-5x-2 [-10, 10, -5, 5]}

Remember that the derivative is a representation of the Inclination of your curve; so when the derivative is zero it means your curve is neither going up nor down...i.e. it is a max or min!!!