What are the values and types of the critical points, if any, of $f (x) = x^{2} - 5 x + 4$ $f(x)=x^2-5x+4$ ?

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Answer 1 · 2016-01-12T08:06:32

A Minimum point $(\frac{5}{2}, - \frac{9}{4})$ $(5/2, -9/4)$

$f (x) = x^{2} - 5 x + 4$ $f(x)=x^2-5x+4$

First derivative $f' (x)=2x -5$

Equate the $f' (x) = 0$

$2x - 5=0$

solve for $x$

$x=5/2$

solve for $y=x^2-5(x)+4$

$y=(5/2)^2-5(5/2)+4$

$y=25/4-25/2+4$

$y=(25-50+16)/4$

$y=-9/4$

What are the values and types of the critical points, if any, of f(x)=x^2-5x+4f(x)=x2−5x+4f(x)=x^2-5x+4?