Question

y= 2x^3 - 15x^2 + 36x - 20 find turning points and show working out

Answer 1

Given:

The function is:

$y=2x^3-15x^2+36x-20$

To find:

The turning points.

Solution:

We have,

$y=2x^3-15x^2+36x-20$

Differentiate the given function with respect to x.

$y'=2(3x^2)-15(2x)+36(1)-(0)$

$y'=6x^2-30x+36$

$y'=6(x^2-5x+6)$

For turning point, $y'=0$.

$6(x^2-5x+6)=0$

$x^2-3x-2x+6=0$

$x(x-3)-2(x-3)=0$

$(x-3)(x-2)=0$

Using zero product property, we get

$x-3=0$ and $x-2=0$

$x=3$ and $x=2$

Therefore, the turning points of the given function are at $x=2$ and $x=3$.