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

1 Answer
Dec 15, 2016

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!!!