Determine The Nature Of The Stationary Points Of The Following Functions I. Y = 1/3x3 - x2 - 3x + 2 II. Y=x3-6x2-15x+16

Here's the derivation for question 6.a: Step 1: Expand the given expression. Y = (2x − 4)(x² + 2x); Y = 2x(x²) + 2x(2x) − 4(x²) − 4(2x); Y = 2x³ + 4x² − 4x² − 8x; Y = 2x³ − 8x; Step 2: Differentiate the expanded expression with respect to x. Recall that d/dx(axⁿ) = naxⁿ⁻¹. dY/dx = d/dx(2x³) − d/dx(8x); dY/dx = 2(3)x³⁻¹ − 8(1)x¹⁻¹; dY/dx = 6x² − 8x⁰; dY/dx = 6x² − 8 The derivative is: 6x² − 8

Determine The Nature Of The Stationary Points Of The Following Functions I. Y = 1/3x3 - x2 - 3x + 2 II. Y=x3-6x2-15x+16

Here's the derivation for question 6.a: Step 1: Expand the given expression. Y = (2x − 4)(x² + 2x); Y = 2x(x²) + 2x(2x) − 4(x²) − 4(2x); Y = 2x³ + 4x² − 4x² − 8x; Y = 2x³ − 8x; Step 2: Differentiate the expanded expression with respect to x. Recall that d/dx(axⁿ) = naxⁿ⁻¹. dY/dx = d/dx(2x³) − d/dx(8x); dY/dx = 2(3)x³⁻¹ − 8(1)x¹⁻¹; dY/dx = 6x² − 8x⁰; dY/dx = 6x² − 8 The derivative is: 6x² − 8

Solved: Determine The Nature Of The Stationary Points Of…

Here's the derivation for question 6.a:

Expand the given expression.
$Y = (2x - 4)(x^2 + 2x)$ $Y = 2x(x^2) + 2x(2x) - 4(x^2) - 4(2x)$ $Y = 2x^3 + 4x^2 - 4x^2 - 8x$ $Y = 2x^3 - 8x$
Differentiate the expanded expression with respect to $x$ .
Recall that $\frac{d}{dx}(ax^n) = nax^{n-1}$ .
$\frac{dY}{dx} = \frac{d}{dx}(2x^3) - \frac{d}{dx}(8x)$ $\frac{dY}{dx} = 2(3)x^{3-1} - 8(1)x^{1-1}$ $\frac{dY}{dx} = 6x^2 - 8x^0$ $\frac{dY}{dx} = 6x^2 - 8$
The derivative is:
$\boxed{6x^2 - 8}$

Determine The Nature Of The Stationary Points Of The Following Functions I. Y = 1/3x3 - x2 - 3x + 2 II. Y=x3−6x2−15x+16

Step-by-step solution

Expand the given expression.

Differentiate the expanded expression with respect to $x$ .

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