Using a calculator to estimate extrema of f(x)=5x³-30x²+45x+5√x

[Nawz]

Homework Statement

Use a calculator to estimate any extrema of this function:
f(x)=5x^3-30x^2+45x+5(sqrt(x))

Homework Equations

The Attempt at a Solution

I don't know how to find it using a calculator.

f'(x)= 15x^2-60x+45+(5/2)x^(-1/2)

 

[HallsofIvy]

If your calculator is a graphing calculator, graph y= f'(x) and see where it crosses the x- axis. Another method of solving such an equation is to use a "Newton's method" or some other numerical method.

 

[rs1n]

Homework Statement

Use a calculator to estimate any extrema of this function:
f(x)=5x^3-30x^2+45x+5(sqrt(x))

Homework Equations

The Attempt at a Solution

I don't know how to find it using a calculator.

f'(x)= 15x^2-60x+45+(5/2)x^(-1/2)

Since you are estimating, you can simply graph f(x) and look for peaks (maxes), troughs (mins), and where the graph changes concavity (inflection points; though most books do not consider this an extremum). The derivative is not really needed, unless you want a more accurate estimate.