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`.