Question

Consider the following functional relations between x and y.

Y = (2x² – 6x-20)²

a) at what values of x will the function have zero slope?

b) identify whether those zero slope points are maximum or minimum values of the function.

Answer 1

$Y = (2x^2 – 6x-20)^2$

The slope is;

$\frac{\Delta Y}{\Delta x}=2(2x^2-6x-20)(4x-6)$

Putting $\frac{\Delta Y}{\Delta x}=0$ ;

Either 2x²-6x-20=0 or 4x-6=0

For 2x²-6x+20=0;

$$x=\frac{6\pm\sqrt{36+160}}{2×2}$$

$x=5,-2$

For 4x-6;

$x=\frac{6}{4}=\frac{3}{2}$

$\therefore$ for $x=-2,5,\frac{3}{2}$ Slope is zero

b)For x=2. Y=0 (min)

For x=5. Y=0 (min)

For x=$\frac{-3}{2}$ Y=42.25 ( max)