Question

Find the slope of the curve y=3x²+6x at x=5

Answer 1

Given :

An equation $y=3x^{2} +6x$

To find :

The slope of the curve.

Step-by-step explanation:

• The slope of the curve can be found by following these steps.
• The given equation is

        $y=3x^{2} +6x$ where x = 5

• Replace x by 5

       $y = 3 (5)^{2} +6(5)$

• Remove the brackets.

        $y = 3(25)+30$

        $y=75+30$

• Add the numerical values.

        $y=105$

• This states that the curve is parallel to x axis.

Final answer :

The slope of the equation is 105.

Answer 2

Answer:

Step-by-step explanation:

Given:

$y = 3x^2 + 6x$

Differentiate w.r.to x

$\frac{dy}{dx} = 6x + 6$

$\boxed{f'(x) = 6x + 6}$

Slope of the tangent at x = 2

f'(5) = (6 × 5) + 6

f'(x) = 30 + 6

f'(x) = 36

Slope of the curve at y = 3x² + 6x at x = 5 is 36